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Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Physical quantities and units of measurement. Marco Caniato Free University of Bozen Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato A physical phenomenon or system can be described through a number of attributes, useful to characterize its nature, state or behavior A physical quantity Q characterizing the system a magnitude or value: |Q| level, intensity Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato The values of a given quantity in different systems can be compared to assess whether they are or not equivalent Comparison of values Kinds or Classes Certain class Certain magnitude Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Measurement is the assignment of a number or symbol to a quantity in order to describe or express its value. To compare quantities of the same class, we can rely on measurement. Comparison of measurements measure same class association with a number Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Example: Quantity, magnitude and class length length length width width width Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Measurement can be direct, when it implies only a comparison between entities of the same class, or indirect, when it is based on relations between the entities to be measured and other measurable quantities. system of empirical relations among elements of the class among elements of the class Q formal correspondence Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Classifications: Ordinal scale. In ordinal scales the set of relations is given by an empirical order system: R = [Q, ~, <, >] relations are complementary if Q1<Q2 then Q2>Q1 any couple of quantities only one of the three is true Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Example: Mohs’ scale of hardness: it permits to measure the hardness of a surface Talc Apatite Diamond absolute hardness 1 absolute hardness 5 absolute hardness 10 Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Measurement can be indirect, when it is based on relations between the entities to be measured and other measurable quantities. They can be measured through either (i) associative or (ii) derived measurement. Associative measurements any quantity non measurable Q Q is ordered within the class Q associated with other measurable quantity X Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Example: Celsius and Fahrenheit Celsius and Fahrenheit scales are based on the relation with the length of the thermometric liquid in the capillary tube. Also the definition of the scale corresponds to a linear scale: two measures are selected for reference temperatures, providing their distance. One of the reference temperatures in the case of Celsius scale is also the arbitrary zero of the scale. Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Measurement can be derived, when the value of quantity to be measured can be expressed in mathematical terms as a function of the values of a set of other measurable quantities, called fundamental or primary quantities. a quantity Q Q = F(X,Y,Z). Q is derived associated to set of quantities X, Y, Z numerical law exists between quantities Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Example: Density Introducing density as a property of a given material, assuming the same value for all objects of the same material. It can be related to the ratio ρ between the mass m of the object and its volume V, such that ρ=m/V is constant for all the objects of the same material. Whenever objects are arranged in order of density, intended as a quantity, they will be ordered according ρ, intended as a measure of density. Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Example: Velocity Velocity can be introduced as a derived quantity, defined as the ratio between the distance travelled and the time duration. = Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato The concept of dimensions can be introduced. In general, but in particular for fundamental quantities, quantities of the same kind of Q have the same dimensions, as a consequence of the fact that those quantities can be compared and measured on the same scale derived quantity Q = Xx Yy Zz (all dimensions) derived measure derived dimension(s) Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Example: Force Force can be said to have the dimensions of a mass times the dimensions of an acceleration. = · Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato When taking a direct measurement, the quantity to be measured is generally compared with a reference one and its multiples or submultiples. length width Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato In both analog instruments and digital instruments, the measurement is affected by approximations leading to uncertain measures. Overall uncertainty expresses the estimated distance between the actual value, which is by definition not known, and the measured one. Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato In such cases uncertainty arises because of the resolution or sensitivity of the instrument. The quality of construction of the instrument can also bring some uncertainty, considering for instance possible approximations in the reproduction of the reference units or in the alignment to the zero of the scale, or the stability of the instrument. Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Two attributes can describe the quality of a measure in terms of uncertainty: accuracy and precision. Accuracy refers to the quality of a measure to be close to the real value. The more accurate, the closer a measure is to the real value. Inaccuracy can be reduced comparing and tuning the instrument with respect to a reference one, in a process named calibration. Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Precision refers to the repeatability of a measurement. The more precise, the less disperse a repeated series of measures is. For a set of measurements, normally distributed, standard deviation can provide a measure of the precision. Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Accuracy and precision can be determined using many methodologies. σ = 1 =1 − graphically 2 ∆ = 1 =1 | regression − | Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Example: comparison of measurement methodologies Methodology System 1 System 2 Parameter 2 Parameter 1 dev. st. r2 dev. st. Parameter 2 Parameter 1 r2 dev. st. r2 dev. st. r2 A 5.9 4.8 0.931 -- -- -- 9.2 7.7 0.931 -- -- -- B 2.8 2.0 0.951 3.0 2.6 0.891 5.4 4.2 0.973 8.22 6.6 0.788 C -- -- -- -- -- -- 2.6 2.3 0.987 8.22 6.6 0.788 D 3.4 3.0 0.959 3.3 3.3 0.902 2.7 2.3 0.990 8.12 6.9 0.826 E 2.4 1.92 0.965 3.0 2.6 0.920 2.3 1.9 0.992 8.15 6.6 0.879 Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Example: comparison of measurement methodologies Q-Q plot. Measurements vs. Std. model. Bare structure Q-Q plot. Measurements vs. TMM. Bare structure Q-Q plot. Measurements vs. simplified FEM. Bare structure 60 60 60 55 55 55 50 50 50 45 45 45 40 40 40 35 35 35 30 30 30 25 25 25 20 20 20 15 15 15 10 10 10 15 20 25 30 35 40 45 50 55 60 10 10 15 20 25 30 35 40 45 50 55 10 60 Q-Q plot. Measurements vs. TMM + Simplified FEM. Bare structure 60 55 50 45 40 35 30 25 20 15 10 10 15 20 25 30 35 40 45 50 55 60 15 20 25 30 35 40 45 50 55 60 Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato When reporting a measure, there are different notations to indicate the uncertainty. It can make some difference when considering analog or digital measurements. Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Consider the choice is for 158.3, then the reading will be: 15.83 cm or 158.3 mm. Where 3 is the estimated and so uncertain digit. Although this intends to be a good estimation of the actual measure, we can report that uncertainty is on the last digit. It also means that the reported measure is actually affected by an estimated uncertainty of ± half the resolution of the instrument: 158.3 ± 0.5 mm Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Imagine the weigh of an object is 24.4 g and it has to be measured on a digital balance with a maximum resolution of 1 g. When the object is put onto the balance, the reading of the display will provide 24 g. It can be supposed at a first approximation that the reported measure is the result from rounding of the actual value, so it will not be possible to argue whether the weigh to be measured is 23.4 or 24.4 g. Therefore, the uncertainty is 0.5 mm. Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato It is worth noting that in both cases measures are expressed with a given number of figures or digits. Not all figures have the same importance and meaning. 145,98000 0.0001583 km, 0.1583 m, 15.83 cm, 158.3 mm 0.024 kg, 24 g 0.024 kg, 24 g 24 g ≠ 24.0 g ≠ 24.00 g Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato For indirect measurement of derived quantities the effect of the uncertainty of each fundamental quantity has to be assessed, taking into account the defining expression. The same happens when performing operations with measures. addition (x ± Δx)+ (y ± Δy) = x+y ±( Δx+ Δy) subtraction (x ± Δx)– (y ± Δy) = x–y ± ( Δx+ Δy) product (x ± Δx) ×∙(y ± Δy) = x × y ± (x Δy + y Δx) division (x ± Δx)/(y ± Δy) = x/y ± (x Δy + y Δx)/(y2) Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Geographical or cultural contexts have consolidated over time the local definition and use of a variety of sets of units of measurement, different not only for the choice of units, but also for the choice of the base and derived quantities, most of the times without paying much attention to their coherence. The process that led to the definition of the International System (SI) started from the metric decimal system. That was introduced in France at the time of the French Revolution, even if after an initiative by the king Louis XVI, with the construction of the platinum samples of meter and kilogram, respectively as a unit of length and mass. 1832 1860 1874 1939 1946 1971 1875 1889 1901 59 Member States and 42 Associate States Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato The International System of Units, has been defined through the choice of a suitable set of base units and of coherent derived units, starting from the corresponding products of powers. The first step in the definition of a system of units, namely the choice of base quantities is implicit in the SI. The definition of an International System of Quantities (ISQ), corresponding to the SI units, is the aim of the international standard ISO/IEC 80000 In the past, different types of definitions for the base units have been used, such as: (i) artefacts; (ii) specific physical states; (iii) idealized experimental prescriptions,; (iv) constants of nature. Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato The 26th meeting of the CGPM (2018) approved the revision of the SI, changing the definition of the kilogram, the ampere, the kelvin and the mole, in order to have all units defined from universal constants Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Seven base units and their associated quantities are then defined from the seven constants. Each quantity has a typical symbol, unit of measurement, unit symbol and dimension. Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical valueof the caesium frequency ∆νCs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz: 1 s = 9 192 631 770 / ∆νCs Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m s−1, where the second is defined in terms of the caesium frequency ∆νCs 1 m = c / 299 792 458 × s = c / 299 792 458 × 9 192 631 770 / ∆νCs Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.626 070 15 × 10−34 when expressed in the unit J s, which is equal to kg m2 s−1,where the metre and the second are defined in terms of c and ∆νCs 1 = % . " #$# %& · %#'() *+ Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato 1 = 1 ℎ 6.626 070 15 · 10123 = 9 192 631 770 9 299 792 458 " 678 9 192 631 770 678 299 792 458" ℎ 678 6.626 070 15 · 10123 · 9 192 631 770 9" " Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Once the base quantities have been chosen, all other quantities, with the exception of counts, are derived quantities, which may be written in terms of base quantities according to the equations of physics. dim Q = Tα Lβ Mγ Iδ Θε Nζ Jη Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Twenty-two of the derived units in the SI have special names Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato All other SI units are combinations of some of these. Some of those whose names and symbols are based on derived units with special names and symbols are reported below Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Prefixes can be used with unit symbols to indicate decimal multiples and submultiples of units of measurement in the range from 10-24 to 1024. In particular only power multiples of 3 are considered, except for the range between 10-3 and 103 for which all multiples are available Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Symbols for both prefixes for powers of ten lower than or equal to 3, then up to kilo (k) and units of measurement with names not deriving from the names of scientists (mol, s, rad, km, etc.) are never capitalized. All other prefixes from mega (M) on or units named after a scientist are always capitalized (N, J, W, A, V, etc.) 23 °C, but not 23°C; 5,6 m, but not 5,6m Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato The internationally recognized symbol % (percent) may be used with the SI. When it is used, a space separates the number and the symbol %. As concerns the algebra of symbols, the following rules hold: 1. Products: N×m, N·m, N m, but never Nm 2. Divisions: m/s2, * , 8+ m·s-2, m s-2, but never m/s/s Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato 1. symbols of prefixes are written before symbols of units, without any blank space or other characters 2. the group made of prefix and symbol is a unique entity, to which power, multiplication or division can be applied to get derived quantities: 1 cm3 = (10-2 m)3 = 10-6 m3, but not 10-2 m3 1 ms-1 = (10-3 s)-1 = 1/(0,001 s), not 10-3 s-1 or 0,001/(1 s)) 3. never use double prefixes 4. never use prefixes alone: 106/m3, but not 1 M/m3 Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato The imperial system is based on different units of measurement for length, mass, temperature, so that also derived units are affected by the base ones. Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Energy and Energy transfer. Marco Caniato Free University of Bozen Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Energy Whether we realize it or not, energy is an important part of most aspects of daily life Energy exists in numerous forms such as thermal, mechanical, electric, chemical, and nuclear E=mc2 Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Energy We are familiar with the conservation of energy principle, which is an expression of the first law of thermodynamics Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Forms of Energy Thermodynamics provides no information about the absolute value of the total energy. It deals only with the change of the total energy, which is what matters in engineering problems In thermodynamic analysis, it is often helpful to consider the various forms of energy that make up the total energy of a system in two groups: macroscopic and microscopic U Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Forms of Energy The macroscopic energy of a system is related to motion and the influence of some external effects such as gravity, magnetism, electricity, and surface tension The energy that a system possesses as a result of its motion relative to some reference frame is called kinetic energy = + =+ = [J] [J] where v is the velocity and m the mass of the moving body where g is gravitation acceleration and z the elevation of the center of gravity [J] Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Forms of Energy Most closed systems remain stationary during a process and thus experience no change in their kinetic and potential energies. ∆ Stationary systems!!!! 0 = + 0 [J] + = [J] Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Internal Energy Internal energy is defined earlier as the sum of all the microscopic forms of energy of a system. It is related to the molecular structure and the degree of molecular activity and can be viewed as the sum of the kinetic and potential energies of the molecules∆ Molecular translation Molecular kinetic rotation Molecular kinetic vibration Electron kinetic rotation Electron and nuclear spin Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Internal Energy The portion of the internal energy of a system associated with the kinetic energies of the molecules is called the sensible energy∆ U Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Internal Energy The internal energy is also associated with various binding forces between the molecules of a substance∆ Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Internal Energy This is a phase-change process. Because of this added energy, a system in the gas phase is at a higher internal energy level than it is in the solid or the liquid phase. The internal energy associated with the phase of a system is called the latent energy. Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Internal Energy An atom consists of neutrons and positively charged protons bound together by very strong nuclear forces in the nucleus and negatively charged electrons orbiting around it. The internal energy associated with the atomic bonds in a molecule is called chemical energy C3H8 + O2 3 CO2 + 4 H2O Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Internal Energy The nuclear forces are much larger than the forces that bind the electrons to the nucleus. The tremendous amount of energy associated with the strong bonds within the nucleus of the atom itself is called nuclear energy Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Internal Energy The forms of energy already discussed, which constitute the total energy of a system, can be contained or stored in a system, and thus can be viewed as the static forms of energy. static dynamic Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Internal Energy The only two forms of energy interactions associated with a closed system are heat transfer and work. Temperature driven Other cases Heat transfer Work Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Mechanical Energy Distinction should be made between the microscopic and macroscopic kinetic energy Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Mechanical Energy The mechanical energy can be defined as the form of energy that can be converted to mechanical work completely and directly by an ideal mechanical device Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Mechanical Energy: example and exercitation A pump transfers mechanical energy to a fluid by raising its pressure and a turbine extracts mechanical energy from a fluid by dropping its pressure Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Mechanical Energy: example and exercitation The ℎ ! of a flowing fluid can be expressed as: . = . " $ + + # 2 [W] Flow energy . ∆ = . & '&( ) + ' ( + − + [W] Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Mechanical Energy: example and exercitation Application to wind turbine: A site evaluated for a wind farm is observed to have steady winds at a speed of 6 m/s. Determine the wind energy per unit mass (i) for a mass of 10 kg and (ii) for a flow rate of 1154 kg/s for air $ 2 = . = . $ 2 = 10 . = 1154 . 6 6 2 /1 2 = 180 3 /1 = 20.8 .7 Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Energy transfer by heat Energy can cross the boundary of a closed system in two distinct forms: heat and work Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Energy transfer by heat Heat is defined as the form of energy that is transferred between two systems (or a system and its surroundings) by virtue of a temperature difference Room hair 25 °C no heat transfer Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Energy transfer by heat Several phrases in common use today heat addition/rejection Heat loss heat absorption resistance heating body heat heat generation heat source Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Energy transfer by heat Heat is energy in transition. It is recognized only as it crosses the boundary of a system 2J Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Energy transfer by heat A process during which there is no heat transfer is called an adiabatic process Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Energy transfer by heat The amount of heat transferred during the process between two states (states 1 and 2) is denoted by Q12, or just Q. Heat transfer per unit mass of a system is denoted q 8= 9 [ 3 ] . Sometimes it is desirable to know the rate of heat transfer instead of the total heat transferred over some time interval 9 = : 9; <= [3] 9 = 9; =[3] [3] ( 45 kJ Q= 45 kJ m = 3 kg ∆ t = 15 s 9; = 675 kW q = 15 kJ/kg Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Energy transfer by work Work, like heat, is an energy interaction between a system and its surroundings The work done per unit time is called power and is denoted W; >= 7 [ 7 = : 7; <= ( 7 = 7; =[3] 3 ] . [3] 45 kJ [3] W= 45 kJ m = 3 kg s= 15 s 7; = 675 kW w = 15 kJ/kg Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Energy transfer by work The generally accepted formal sign convention for heat and work interactions is as follows: heat transfer to a system and work done by a system are positive; heat transfer from a system and work done on a system are negative. Qout Win -Q -W Qin Wout +Q +W Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Energy transfer by work Heat and work are energy transfer mechanisms between a system and its surroundings and there are many similarities between them: 1) Boundaries p 1 2) Systems possess energy, but not heat or work 3) Both are associated with a process, not a state 2 4) Both are path functions 3 7 V Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Energy transfer by work Path functions have inexact differentials designated by the symbol δ. Therefore, a differential amount of heat or work is represented by δ Q or δ W, respectively, instead of dQ or dW Properties, however, are point functions (i.e., they depend on the state only, and not on how a system reaches that state) and they have exact differentials designated by the symbol d p 1 2 : <@ = @+ − @ = ∆@ + : B7 = 7+, + Not ∆W!!! 3 7 V Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Training Baking a cake in a oven. Heat transfer? Work? Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Training Baking a cake in a oven. Heat transfer? Work? Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Training Baking a cake in a oven. Heat transfer? Work? Engineering Thermodynamics and Heat and Mass Transfer Prof. Marco Caniato Mechanical work There are several different ways of doing work, each in some way related to a force acting through a distance W = Fs W = D+ E<1 Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Thermodynamics: basic concepts. Marco Caniato Free University of Bozen Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Thermodynamics Thermodynamics can be defined as the science of energy. Although everybody has a feeling of what energy is, it is difficult to give a precise definition for it. Energy can be viewed as the ability to cause changes Conservation of energy: during an interaction, energy can change from one form to another but the total amount of energy remains constant Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Thermodynamics All activities in nature involve some interaction between energy and matter; thus, it is hard to imagine an area that does not relate to thermodynamics in some manner Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato System and control Volumes A system is defined as a quantity of matter or a region in space chosen for study surroundings Boundary Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato System and control Volumes Systems may be considered to be closed or open, depending on whether a fixed mass or a fixed volume in space is chosen for study mass Closed system energy Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato System and control Volumes Consider the piston-cylinder device Closed system Gas 1 kg, 2 m3 Gas 1 kg, 1 m3 Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato System and control Volumes An open system, or a control volume, as it is often called, is a properly selected region in space. It usually encloses a device that involves mass flow such as a compressor, turbine, or nozzle. Control volume Real boundary Imaginary boundary Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato System and control Volumes A control volume can be fixed in size and shape, as in the case of a nozzle, or it may involve a moving boundary Moving boundary Fixed boundary Control volume Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato System and control Volumes Example of open system Hot water Control volume (water heater) Cold water Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Property of a system Any characteristic of a system is called a property. Some familiar properties are pressure P, temperature T, volume V, and mass m. extensive m m½ m ½m V V½ V ½V T T T T P P P P ρ ρ ρ ρ intensive Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato State and Equilibrium Consider a system not undergoing any change. At this point, all the properties can be measured or calculated throughout the entire system, which gives us a set of properties that completely describes the condition, or the state, of the system. m = 2 kg m = 2 kg T = 25 °C V = 1.5 m3 T = 25 °C V = 3 m3 Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato State and Equilibrium There are many types of equilibrium and a system is not in thermodynamic equilibrium unless the conditions of all the relevant types of equilibrium are satisfied Thermal equilibrium 20 °C 30 °C 33 °C 35 °C 32 °C 32 °C 32 °C 32 °C Mechanical equilibrium Phase equilibrium Chemical equilibrium oil C H8 + O2 water 3 3 CO2 + 4 H2O Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Process and cycles Any change that a system undergoes from one equilibrium state to another is called a process, and the series of states through which a system passes during a process is called the path of the process paths Property A state 4 state 1 state 2 state 3 Property B Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Process and cycles When a process proceeds in such a manner that the system remains infinitesimally close to an equilibrium state at all times, it is called a quasistatic, or quasi-equilibrium, process Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Process and cycles The prefix iso- is often used to designate a process for which a particular property remains constant. An isothermal process, for example, is a process during which the temperature T remains constant; an isobaric process is a process during which the pressure P remains constant; and an isochoric (or isometric) process is a process during which the specific volume v remains constant. Property A Property B Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato The Steady-Flow Process The terms steady and uniform are used frequently in engineering, and thus it is important to have a clear understanding of their meanings. The term steady implies no change with time. The opposite of steady is unsteady, or transient. The term “uniform”, however, implies no change with location over a specified region 27 °C 22 °C Control volume 25 °C mcV = const. EcV = const. Mass in 29 °C 20 °C Mass out Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Temperature Several properties of materials change with temperature in a repeatable and predictable way and this forms the basis for accurate temperature measurement Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Temperature. Zeroth principle At equilibrium, heat transfer stops, and the two bodies are said to have reached thermal equilibrium. The equality of temperature is the only requirement for thermal equilibrium. If two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other 100 °C 20 °C 60 °C 60 °C Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Exercises! Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Thermodynamics Why does a car pick up speed on a downhill road even when it is not using the engine? Does this violate the conservation of energy principle? Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Thermodynamics A friends of yours states that a cup of cold tee on his table warmed up to 50°C by picking up energy from the surrounding air, which is at 20°C. Is there any truth to his claim? Does this process violate any thermodynamic laws?? Conservation of energy: during an interaction, energy can change from one form to another but the total amount of energy remains constant Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Thermodynamics A large fraction of the thermal energy generated in the engine of a car is rejected to the air by the radiator through the circulating water. Should the radiator be analyzed as a closed system or as an open system? T1 Mass out T2 T3 Mass in T5 T4 Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Thermodynamics A friends of yours ask you to get a can of soft drink from the fridge. He put it into the refrigerator so that it would cool. Would you model the can of soft drink as a closed system or as an open system? mass Closed system energy Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Thermodynamics What is the difference between intensive and extensive properties? extensive m m½ m ½m V V½ V ½V T T T T P P P P ρ ρ ρ ρ intensive Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Thermodynamics For a system to be in thermodynamic equilibrium, do the temperature and the pressure have to be the same everywhere? Thermal equilibrium 20 °C 30 °C 33 °C 35 °C 32 °C 32 °C 32 °C 32 °C Mechanical equilibrium Phase equilibrium Chemical equilibrium oil C H8 + O2 water 3 3 CO2 + 4 H2O Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Thermodynamics What is a quasi-equilibrium process? What is its importance in engineering? Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Thermodynamics What is a steady-flow process? 27 °C 22 °C Control volume 25 °C mcV = const. EcV = const. Mass in 29 °C 20 °C Mass out Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Thermodynamics Define the isothermal, isobaric, and isochoric processes What is the zeroth law of thermodynamics? 100 °C 20 °C 60 °C 60 °C Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato First law of thermodynamics Marco Caniato Free University of Bozen Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato First law of thermodynamics The first law of thermodynamics, also known as the conservation of energy principle, provides a sound basis for studying the relationships among the various forms of energy and energy interactions The first law of thermodynamics states that energy can be neither created nor destroyed during a process; it can only change forms Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato First law of thermodynamics For all adiabatic processes between two specified states of a closed system, the net work done is the same regardless of the nature of the closed system and the details of the process Chemical work Mechanical work Electrical work Nuclear work Elastic work … Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato First law of thermodynamics A major consequence of the first law is the existence and the definition of the property total energy E. Change in the p property of the 1 system Pi Pf 2 Vi Vf V Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato First law of thermodynamics Consider some processes that involve heat transfer but no work interactions. The boiled egg is a good example for this case 2J Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato First law of thermodynamics Consider some processes that involve heat transfer but no work interactions. The water boiling is a good example for this case 1kJ 20 k J NET HEAT TRANSFER = 19 kJ Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato First law of thermodynamics Now consider a well-insulated (i.e., adiabatic) room heated by an electric heater as system Win = 8 kJ ∆E = 8 kJ Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato First law of thermodynamics The conservation of energy principle again requires that the increase in the energy of the system be equal to the boundary work done on the system. Win = 8 kJ ∆E = 8 kJ Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Energy balance The conservation principle can be rewritten as follows: The net change (increase or decrease) in the total energy of the system during a process is equal to the difference between the total energy entering and the total energy leaving the system during that process Ein - Eout = ∆ Esystem Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Energy balance The determination of the energy change of a system during a process involves the evaluation of the energy of the system at the beginning and at the end of the process, and taking their difference. Efinal - Einitial = E2 – E1 = Ein - Eout = ∆ Esystem stationary ∆ Usystem = ∆ Esystem Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Mechanisms of Energy Transfer Energy can be transferred to or from a system in three forms: heat, work, and mass flow. Energy interactions are recognized at the system boundary as they cross it, and they represent the energy gained or lost by a system during a process. Heat molecular movement and storage Work not driven by temperature Mass flow movement of mass in an open system Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Mechanisms of Energy Transfer Energy can be transferred in the forms of heat, work, and mass, and that the net transfer of a quantity is equal to the difference between the amounts transferred in and out, the energy balance can be written more explicitly ∆ Esystem = (Qin – Qout ) + (Win – Wout ) + (Efinal - Einitial) Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Mechanisms of Energy Transfer For a closed system undergoing a cycle, the initial and final states are identical, and thus ∆ Esystem = 0 p W=Q V Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Mechanisms of Energy Transfer Example: mixing hot water in a pan Qout = 250 kJ Win = 100 kJ Q = 600 kJ Determine the final internal energy Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Energy balance Example: mixing hot water in a pan Efinal - Einitial = E2 – E1 = Ein - Eout = ∆ Esystem stationary ∆ Usystem = ∆ Esystem U2 – U1 = Ein - Eout U2 – U1 = Win - Qout Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Energy balance Example: mixing hot water in a pan U2 – U1 = Win - Qout U2 – 600 = 100 - 250 U2 = 100 – 250 + 600 U2 = 450 kJ Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Mechanisms of Energy Transfer Example: moving fan Win = 18 W Determine the final air velocity . m = 0.2 kg/s Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Energy balance Example: moving fan Efinal - Einitial = E2 – E1 = Ein - Eout = dEsystem . . Efinal - Einitial . Win,electric stationary . . . . = E2 – E1 = Ein - Eout = 0 . . = m Ekinetic,out = m v2 / 2 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Energy balance Example: moving fan = , = · . = 6.7 m/s Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Energy balance Example: light in an office: fluorescent and led 40 lamps, 10 hours, 40 lamps, 10 hours, 60 W, 320 days/years 20 W, 320 days/years Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Energy balance Example: light in an office: fluorescent and LED Efinal - Einitial = E2 – E1 = Ein - Eout = ∆Esystem Win,electric,fluo = 60 x 40 x 10 x 320 = 7680 kW Win,electric,LED = 20 x 40 x 10 x 320 = 2560 kW Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Efficiency Performance or efficiency, in general, can be expressed in terms of the desired output and the required input = η= " #$ % &' &' ( )&$ % $ &' Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Efficiency Example: Water heater Heat losses = 10 % η = 100% Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Efficiency Example: Water heater Heat losses = 6 % η = 100% Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Efficiency Example: Water heater η = 55% Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Efficiency the efficiency of equipment that involves the combustion of a fuel is based on the heating value of the fuel, which is the amount of heat released when a unit amount of fuel at room temperature is completely burned and the combustion products are cooled to the room temperature Combustion gases * = +, 21500 kJ/kg air 1 kg propane room temperature Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Efficiency Most fuels contain hydrogen, which forms water when burned, and the heating value of a fuel will be different, depending on whether the water in combustion products is in the liquid or vapor form C3H8 + O2 Low heating value 3 CO2 + 4 H2O + HEAT! high heating value Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Efficiency Example : gas heat generator. Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Efficiency Example: electrical generator. A generator is a device that converts mechanical energy to electrical energy, and the effectiveness of a generator is characterized by the generator efficiency, which is the ratio of the electrical power output to the mechanical power input = - . / 0 1 234 56 731345 4 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Efficiency Example: lighting. Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Efficiency of mechanical and electrical devices The transfer of mechanical energy is usually accomplished by a rotating shaft, and thus mechanical work is often referred to as shaft work. A pump or a fan receives shaft work (usually from an electric motor) and transfers it to the fluid as mechanical energy. 3-2 = 89 :,;< 89 :, = 89 :, =8 ;>> 89 :, = 1- 8 ;>> 89 :, Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Efficiency of mechanical and electrical devices Example: rotating shaft 3-2 = ? ℎ $ ℎ A BC $ D 3-2,01 # 'ℎ A&$% ∆D ℎ A&$% = F #ℎ ' $ Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Efficiency of mechanical and electrical devices Example: turbine 3-2 = ? ℎ $ ℎ A D 3-2, BC $ # 'ℎ F #ℎ = A&$% ∆D ' &' ℎ A&$% Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Efficiency of mechanical and electrical devices Example: rotating shaft 3-2 = G3-2510-256 31347H 01-435/3 I 23 I6 0J 89 :, = · KL⁄ N O34 504 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Efficiency of mechanical and electrical devices motor efficiency and generator efficiency should not be confused with mechanical efficiency 3-2 = P P 4 3-2 = 4.013 731345 4 motor fan generator turbine Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Efficiency of mechanical and electrical devices Example: hydraulic turbine generator turbine Water flow 3500 kg/s 30 m Generator 836 kW and η=0.94 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Efficiency of mechanical and electrical devices Example: hydraulic turbine generator 0 . ∆D = . NL =NQ R + KLL =KQL 0 0 +B T −T ∆D = 30 · 9.81 · 3500 = 1,03 ?F = 1030 ^F K34566 = 4.013=731345 4 = VW V = 0.811 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Efficiency of mechanical and electrical devices Example: hydraulic turbine generator 4.013 = < _ a 3-2 . = `a b ; = b ; 89 :,;< 89 :, = . .cd = 0.85 >:be . 8 F/25I = 0.8 · 1030 = 824 kW Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 1 It is assumed that a person at rest transfers an average heat output of 100 W to the environment and that in a theatre containing 1800 people, the air conditioning system stops to function. Let’s assume that the external walls of the theatre are adiabatic. 1.Calculate the internal energy variation of the air in the theatre after 15.0 minutes. 2.Which is the internal energy variation for the system containing air and people? Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 1 Calculate the internal energy variation of the air in the theatre after 15.0 minutes. system=air The variation in internal energy is calculated by applying the First Principle of Thermodynamics ∆U = Q - L where L = 0 because the walls of the system are rigid and non-deformable, so there is no change in volume ∆U = Q Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 1 Q is the heat that a person exchanges with the surrounding environment, due to physiological mechanisms and mechanical activity, and its value depends on the type of activity (sedentary or moving). P = Q / ∆t So the total exchanged heat is Seconds!!! Q = P ∆t Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 1 Take into account the number of present people! Q = 100W 900s 1800 people Q = 100W 900s 1800 people = 162 MJ Thus ∆U = Q = 162 MJ Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 1 Which is the internal energy variation for the system containing air and people. system=air + theatre L = 0 because the boundaries of the system are rigid and non-deformable, so there is no change in volume Q = 0 because the boundaries of the system are adiabatic, so there is no heat exchange ∆U = 0 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 2 A closed container with rigid and fixed walls contains 700 liters of water in a liquid state at a temperature of 40°C. A cylindrical metal body (diameter D = 45 cm and height H = 55 cm) is subsequently immersed in the container at a temperature of 95°C, with a density of 4000 kg/m3 and specific heat 500 J/ kg K. Determine the temperature of the water and the metal at equilibrium, assuming that the heat dispersed to the external environment is not taken into account. It should be remembered that for water the density is 1000 kg/m3 and the specific heat is 4.2 kJ/ kg K. Let’s assume that the container is insulated both thermally and mechanically. Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 2 Applying the First Principle of Thermodynamics to the whole system (water + metal) and considering that the tank walls (system boundary) are adiabatic and fixed, ∆U = Q – L = 0 Therefore, using the additive property of the internal energy (the internal energy of the system is equal to the sum of the internal energies of its components): ∆U = ∆Uwater + ∆Umetal = 0 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 2 1000 *700 * 4.2 * (te - 40)+ 4000* h ∗ + ∗ (" ⁄2) *0.5 (te – 95) = 0 te = 43.1 °C Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 3 Let us consider a thermally insulated container, so that we can suppose that the heat exchange between system and environment is null (Q = 0): in this way the phenomena at the edges are neglected. The container contains 100 l of H2O agitated by a propeller connected to an electric motor. Consider that the transformation takes place under conditions of constant pressure and P= 368 W be the power supplied by the engine and t = 20 min is be the time for which the engine is kept in operation. Determine the ∆ U internal energy variation of the system. Moreover, knowing that the specific heat of the water is cp= 4.2 kJ/ kg K at atmospheric pressure, and that the initial temperature of the system is Tin = 20°C, calculate the final temperature (Te) at the end of mixing. Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 3 ∆U = Q – L No variation in temperature, no heating added and/or exchanged ∆U = – L ∆U = – L = – P * dt = 368 W * 20 min * 60 = 441.6 KJ Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 3 m3 = m01 + ∆n P lm l' ∆U = P ∆U = P (m3 = 293.15 + − m01 ) 441600 = 294.2 p 4200 ∗ 100 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Mechanisms of heat transfer Part 1 Marco Caniato Free University of Bozen Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Mechanisms of heat transfer Heat can be transferred in three different ways: conduction, convection, and radiation 2J Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction Conduction is the transfer of energy from the more energetic particles of a substance to the adjacent less energetic ones as a result of interactions between the particles Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction Conduction is verified when there is no thermal equilibrium ⃗=− Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction λ is defined as thermal conductivity of a material Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction thermal conductivity - fluids = general = fluids Reference parameter Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction λ is defined as thermal conductivity of a material Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction thermal conductivity - solids phonons = solids Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction General equation = T (x,y,z,t) ⃗=− ( , , , ) 0 − = Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction General equation 0 + Variation of ⃗ in space and time ⃗=− = Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction General equation 0 =− Thermal inertia -5 °C +20 °C Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction General equation 0 =− 0 0 + + =0 y x z Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction General equation =0 = +! Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction Determining A e B constants T " 0 = T2= +20 0 " °C T1= 0 °C z 0+! =! = +! = + " Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction Determining A e B constants " 0 =! = + " " =! − = −# $ " " = −− " " =! − " = Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction Propagation path for monodimensional case T = −# − " T2= +20 °C T1= 0 °C z Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction Propagation path for monodimensional case. Multilayer =− T Ti Ti Ti+1 Ti+1 λn λ2 Tn+1 z =− λ1 =− " − " − & Tn % − '" Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction Propagation path for monodimensional case. Multilayer = −( T *+" 1 * ( − '" ) * Tn Ti λn Tn+1 Ti+1 λ2 λ1 z Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Mechanisms of heat transfer Part 2 Marco Caniato Free University of Bozen Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Mechanisms of heat transfer: convection Convection is the mode of energy transfer between a solid surface and the adjacent liquid or gas that is in motion and it involves the combined effects of conduction and fluid motion. Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection Convection is called forced convection if the fluid is forced to flow in a tube or over a surface by external means. In contrast, convection is called free (or natural) convection if the fluid motion is caused by buoyancy forces induced by density differences due to the variation of temperature in the fluid 2J Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection Convection can be considered including a fluid without phase-change (single-phase outflow convection) or phase change, such as condensation and vaporization. Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection it is useful to distinguish between flow regimes. The laminar regime and turbulent regime Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection In the heat exchange with the limiting surface, it has a great relevance to precisely know the layer of fluid closest to it, i.e. the boundary layer tp h tf w Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection Let’s proceed to analyze the Newton law. Boundary condition x Tp Tf = = ( − ) Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection How to determine α? The knowledge of the temperature field in the fluid is a prerequisite for the calculation of the convection coefficient. This can only be determined from the velocity field. General dimensional empirical approach! Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection Let’s assume that the convection coefficient is a function of n quantities = ……….. = 15625 separate tests!!!! Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection Similarity theory or dimensional analysis = ……….. = ……….. Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection Monomial multiplication: dimensionless group (-2ab) x (5a2) x (3ab2) ∏ = · ……… · ! Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection By defining the n quantities in terms of their relationship with the m fundamental quantities it is possible to write " ∏ = # ∏ =# $ $ =# $% ·. . .· $%' #& · ……… · $ ' #& * ….* $! · … … … · #& ' ! ( = 1, . . ., n · ……… · # $ $! · ……… · * ….* $!' ! $!' #& ! Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection Dimensionless condition + + & … + … … + & ℎ · … ℎ 0 = … 0 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection Buckingham theory: if there is a physically meaningful equation involving a certain number n of physical variables, then the original equation can be rewritten in terms of a set of p = n − k dimensionless parameters constructed from the original variables. T L .1 .2 M .3 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Mechanisms of heat transfer: convection Based on the theoretical model of the phenomenon, also confirmed by extensive experimental evidence, the convection coefficient is dependent on: tp h tf w Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection Convection coefficient can be expressed as: = ∏ =# ∏ =8 $ 1, 3, 4, 5, 6 , 7 * ….* $! ·3 9 ·7 ! : · ……… · ·1 ; ·4 < $ ' #& ·5 = · * ….* $!' ! > Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection The fundamental quantities on which the considered quantities depend are the length L, the mass M, the time t, and the temperature T 8 L M t T 3 0 1 1 0 −3 −1 1 0 7 2 0 −2 1 1 4 1 0 0 0 −3 1 0 0 5 −1 1 1 1 −1 −3 0 −1 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection Dimensionless multiplication 0 1 1 0 −3 −1 1 0 2 0 −2 1 . 1 0 0 0 −3 1 0 0 −1 1 1 1 −1 −3 0 −1 ℎ ℎ? ℎ@ ℎA ℎB ℎC ℎD = 0 0 0 0 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection Dimensionless multiplication ℎ? + 2ℎ@ + ℎA − 3ℎB − ℎC + ℎD = 0 ℎ + ℎB + ℎC + ℎD = 0 −3ℎ − ℎ? − 2ℎ@ − ℎC − 3ℎD = 0 − ℎ − ℎ@ − ℎD = 0 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection Given the rank of the matrix, which is equal to 4, the values of three of the hi variables can be set arbitrarily, the remaining four stay non-dependent . 0 0 ℎ? + 2ℎ@ + ℎA − 3ℎB − ℎC + ℎD = 0 1 ℎ + ℎB + ℎC + ℎD = 0 1 0 1 0 0 −3ℎ − ℎ? − 2ℎ@ − ℎC − 3ℎD = 0 − ℎ − ℎ@ − ℎD = 0 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection Given the rank of the matrix, which is equal to 4, the values of three of the hi variables can be set arbitrarily, the remaining four stay non-dependent . 0 + 0 + ℎA − 3ℎB − ℎC + ℎD = 0 ℎA − 3ℎB − 0 − 1 = 0 ℎA = 1 1 + ℎB + ℎC + ℎD = 0 1 + ℎB + 0 − 1 = 0 ℎB = 0 −3 − 0 − 0 − ℎC − 3ℎD = 0 ℎC = 3 − 3 ℎC = 0 −1 − 0 − ℎD = 0 ℎD =-1 ℎD =-1 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection three dimensional products are obtained whose exponents result from the three solutions identified Π1 Π2 Π3 ℎ 1 0 0 ℎ? 0 1 0 ℎ@ 0 0 1 ℎA 1 1 0 ℎB 0 1 0 ℎC ℎ D 0 −1 −1 0 1 −1 = ? @ 81 314 = 5 = 7 5 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Forced convection In conclusion, Buckingham's theorem allows us to replace the analysis of the general function with the dimensional one = 1, 3, 4, 5, 6 , 7 F= GH, IJ Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Forced convection: examples Some empirical relations F = K GH $ IJ L F = 0.332 GH M.B IJ M.@@ F = 0.0296 GH M.P IJ M.@@ ……… Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Natural convection Some empirical relations Thermal dilatation = 1, Q · R · ∆T, 4, 5, 6 , 7 As before = 81 ? 4? Q R ∆T U@ = 5? @ = 7 5 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Natural convection: examples Some empirical relations F = V #J & IJ & G+ = #J IJ Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction plus convection W T=f,e 6 X ( ? −Tf,i ) Tp W = 6 X ( ?− ) ( Y− ") W= GZ[Z Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction plus convection ( Y− ") W= GZ[Z ( Y− ") W= 1 \ 1 + + X YX "X X( Y − " ) W= 1 \ 1 + + Y " Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Mechanisms of heat transfer Part 4 Marco Caniato Free University of Bozen Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Mechanisms of heat transfer: radiation Radiation is the energy emitted by matter in the form of electromagnetic waves (or photons) as a result of the changes in the electronic configurations of the atoms or molecules 2J Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Radiation Radiation is a volumetric phenomenon and all solids, liquids and gases emits, absorbs, or transmits radiation of varying degrees Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Radiation Focus on electromagnetic waves Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Radiation Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. A plane linearly polarized wave propagating from left to right. The electric and magnetic fields in such a wave are in-phase with each other, reaching minima and maxima together Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Radiation The radiation impinging a system is generally divided into three components: a certain amount is absorbed, another is reflected and the remaining part is transmitted through the system. Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Radiation In opaque systems, the transmitted part is negligible and the thermal radiation can be analysed as a surface phenomenon. Black surface (black body) J J Gr G E G Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Radiation Specific frequency behavior. Example: traditional glass τ 0.9 0.1 1µm λ Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Radiation The maximum rate of radiation that can be emitted from a surface at an absolute temperature Ts is given by the Stefan–Boltzmann law as (heat flux rate) for black body: = = 5.67 · 10 A is the surface area Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Radiation What is a black body? - no body at a certain temperature can emit at a certain date wavelength plus energy of a black body at the same temperature - a black body absorbs all of the incident energy regardless of the wavelength and direction - the emission intensity is independent of direction (diffuse emission) (Lambert’s laws) Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Radiation Plank’s law correlates monochromatic emission intensity and monochromatic emission to wavelength and temperature. = 1 −1 Black body 3.742 10 % $ ⁄ = 1.439 10 % ⁄ = Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Radiation Wien's displacement law states that the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature. Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Radiation Example: greenhouse effect 6000 °K Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Radiation Example: greenhouse effect λ Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato radiation Black body / grey body: focus Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato radiation Prevost's law defines in a simple way the energy that is exchanged by radiation black body ( = ) − * =+ grey body =+ , = +( , ) Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato radiation General law for radiation: black body a1 = 1 a2 = 1 = T1 > T2 ( - ) Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato radiation General law for radiation: grey body a1 ≠ 1 a2 ≠ 1 = T1 > T2 ( − 1 1 + −1 + + ) Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato radiation General law for radiation: EXAMPLE of grey bodies a1 = 0.1 a2 = 0.1 = 300°K > 270°K ( − 1 1 + −1 + + ) Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato radiation General law for radiation: EXAMPLE of grey bodies a1 = 0.1 a2 = 0.1 10 · 5.67 · 10 (300 − 270 ) = 1 1 + −1 0.1 0.1 300°K > 270°K Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato radiation General law for radiation: EXAMPLE of grey bodies a1 = 0.1 a2 = 0.1 0.9 0.9 0 0 = 83 W 0 3 300°K > 270°K 3 3 = 156 W = 1292 W Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato radiation General law for radiation = 4(+ , + = 4 + ,+ = 4 + ,+ , )( , , , , , − ) + ( + ( Cost? − + ) ) − Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato radiation General law for radiation T1 = 300 K T2 = 270 k + + = 163470 − ≅ T1 = 330 K = 30 K x2 T2 = 270 k + + = 182470 K − = 60 K Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato radiation General law for radiation = 4 + ,+ , , ( + =+ 5 + − ) − Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Global mechanism of heat transfer rad rad conv 89; =< ) − 0 conv cond *67 rad rad Te Ti = +*67 897 = : ) − ) − 0 0 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato radiation General law for radiation ) =< ) = <) 0 =< 0 = <0 ) ) ) ) − 0 − − − + +*67 ) − + +*67 ) − 0 0 0 0 0 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato radiation Example: radiation from a person 19 °C 89; = 6 · 1.3 · 28 − 19 *67 = · · 1.3 · 301 − 292 28 °C =8= = 70.2 + 65.7 = 135.9 W Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Lecture 5. Mechanisms of heat transfer Part 8. Exercises Marco Caniato Free University of Bozen Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction: A flat wall consists of three layers in series of bricks 15 cm thick, concrete 10 cm thick and plaster 2 cm thick respectively. The temperature of the outer face of the brick wall is 25 °C and the temperature of the outer face of the plaster is 5 °C. Consider the thermal conductivity of bricks, concrete and plaster of 0.70, 1.6 and 1.0 W/mK respectively. The specific heat flow and temperature of the brick-concrete wall interface is to be evaluated. 25 °C 5 °C Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction: 1 = + − + 1 = 25 − 5 0.15 0.1 0.02 + + 0.7 1.6 1.0 = 67.4 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction: In order to evaluate the temperature of the T1-2 brick-concrete wall interface we consider the heat flow transmitted by conduction only through the brick layer: = 1 25 − stationary = 67.4 = Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Conduction: In order to evaluate the temperature of the T1-2 brick-concrete wall interface we consider the heat flow transmitted by conduction only through the brick layer: 1 67.4 = 25 − 0.7 0.15 = 10.5 °! Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection: A pipe with an inner diameter D = 30 mm and a length of L = 1 m is run through by water at the average temperature Tf = 90 °C. If the water velocity is u = 1 cm/s and the wall temperature Tp = 40 °C, determine the heat flow given to the wall by convection. For the evaluation of the water-tube convective heat exchange coefficient, use the following heat exchange correlation: ) "# = 1.86 %& Pr * +. Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection: Temperature K Thermal Density Specific heat conductivity kg/m3 ρ cp J/kg °C λ W/m °C Dynamic Thermal diffusivity m2/s α diffusivity kg/m2 µ 90 °C 40 °C cinematic diffusivity m2/s γ Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection: , =-ℎ / − 0 "# · 2 =) ) 1.86 %& Pr * ,=) / − − 0 +. · / 0 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection: 3 ·# ·) %& = 4 56 = 9 : = / − 2 0 78 · 4 = 65 °! = 338.15 < Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection: 9 : = / − 2 0 = 65 °! = 338.15 < Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection: Linear interpolation: >+ − > = − = =+ = > −> > = >+ =+ > = += Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection: Linear interpolation: =+,@ 338.15 − 320 980 − 989 = + 989 340 − 320 =+,@ = 980.83 =+,B = ⋯ =+, = ⋯ =+,D = ⋯ Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection: 3 ·# ·) %& = = 695 4 56 = E ·4 = 2.69 ∗ 10 ) "# = 1.86 %& Pr * + +. = 7.02 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Convection: = ℎ= ℎG)* / − / 0 − "# · 2 =) 0 "# · 2 =) = 726.6 / − 0 / − 0 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Radiation: A black body is at a constant temperature of 300 °C. Evaluate the specific heat flux emitted by radiation. Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Radiation: = H+ I = 5.67 · 10 J · 300 + 273.15 4 = 6118 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato 200 °C 50 °C →L H+ I − LI = 1 1 + −1 M ML = stationary L→ H+ LI − I = 1 1 + −1 M ML Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato H+ I − LI H+ LI − LI = 1 1 1 1 + −1 + −1 M M ML ML 1 1 1 1 I I + −1 − L − + −1 M ML M ML 1 1 1 1 + −1 + −1 M ML M ML I L − I =0 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato 1 1 1 1 I I + −1 − L − + −1 M ML M ML 1 1 1 1 + −1 + −1 M ML M ML All constant – No variables :N + :O −1 I L − I =0 :P + :O −1 =k Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato 1 1 + −1 M ML 1 1 + −1 M ML 1 1 + −1 M ML I I − − I I L − I L I L 1 1 − + −1 M ML Q 1 1 − + −1 M ML Q 1 1 − + −1 M ML I L I − =0 I L − I Q =0·Q I L − I =0 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato I 1 1 + −1 − M ML I 1 1 + −1 + M ML I 1 1 + −1 − M ML I L I 1 1 + −1 = M ML 1 1 + −1 + M ML I I L = I L I 1 1 + −1 + M ML I L I 1 1 + −1 + M ML 1 1 + −1 = M ML I L 1 1 + −1 =0 M ML I L 1 1 + −1 M ML 1 2 1 + + −2 M ML M 1 1 1 1 + −1 + I + −1 ML ML M M 1 2 1 + + −2 M ML M Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato I I L = 1 1 1 1 + −1 + I + −1 M M ML ML 1 2 1 + + −2 M ML M Remember: use Kelvin!!!!!! R L = 473.15I 1 1 1 1 + − 1 +323.15I + −1 0.1 0.1 0.1 0.1 = 417.9 < 1 2 1 + + −2 0.1 0.1 0.1 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Absence of intermediate plane: 200 °C → 50 °C → = - · H+ I − I = 1 1 + −1 M M 473.15I − 323.15I 1 1 + −1 0.1 0.1 5.67 · 10 J = 117 S Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato presence of intermediate plane: 200 °C →L 50 °C →L = L→ Heat fluxes are the same so it is the same to compute the first or the second one H+ I − LI H+ LI − I = = = 1 1 1 1 + −1 + −1 M ML ML M L→ Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato presence of intermediate plane: 200 °C →L = L→ 50 °C → = 473.15I − 417.19I 1 1 + −1 0.1 0.1 5.67 · 10 J = 58.5 S Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato The ideal gas Marco Caniato Free University of Bozen Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Pure substances A substance that has a fixed chemical composition throughout is called a pure substance N2 Air vapour air oil water Liquid air water Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Pure substances There are many practical situations where two phases of a pure substance coexist in equilibrium. State 1 State 2 P= 1 atm P= 1 atm T T Compressed liquid = 20 °C = 100 °C Saturated liquid Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Pure substances Once boiling starts, the temperature stops rising until the liquid is completely vaporized State 3 State 4 P= 1 atm P= 1 atm T T saturated vapor Saturated liquid = 100 °C = 100 °C Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Pure substances Once the phase-change process is completed, we are back to a single phase region again superheated vapor State 5 P= 1 atm T = 100 °C Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Pure substances This constant-pressure phase-change process is illustrated on a T-v diagram Saturation temperature Saturated mixture Superheated vapor Temperature Compressed liquid Volume Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Pure substances The variations of properties during phase-change processes are best studied and understood with the help of property diagrams CRITICAL POINT CRITICAL POINT P2 = cost P Superheated vapor region T2 = cost P= 1 MPa P1 = cost T = 150 °C Saturated liquid-vapor region V Compressed liquid region T Superheated vapor region T1 = cost Saturated liquid-vapor region V Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Pure substances the P-T diagram of a pure substance is often called the phase diagram since all three phases are separated from each other by three lines Substances that expand on freezing Substances that contract on freezing 4 °C LIQUID P V Triple point VAPOR 0 4 T [°C] T Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Entalpy In the analysis of certain types of processes, particularly in power generation and refrigeration, we frequently encounter the combination of properties u + Pv. For the sake of simplicity and convenience, this combination is defined as a new property, enthalpy, and given the symbol h u2 P2 V2 u1 P1 V1 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato The ideal-gas equation of state Any equation that relates the pressure, temperature, and specific volume of a substance is called an equation of state PV=RT Gas constant R = Ru / M Molar mass m=MN R = kB NA Same for all substances Universal Gas Constant R = 8.3163 J / mol K Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato The ideal-gas equation of state Determine the mass of the air in a room whose dimensions are 4 m x 5 m x 6 m at 100 kPa and 25 °C. Air molecular weight: 28.9647 kg/kmol 5m P = 100 kPa T = 25 °C m=? 6m 4m Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato The ideal-gas equation of state V = 4 m * 5 m * 6 m = 120 m3 PV=mRT R = Ru / M P V = m Ru T / M P V = m Ru T / M m = P V M / Ru T Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato The ideal-gas equation of state V = 4 m * 5 m * 6 m = 120 m3 100 · 120 · 28.9647 = = 140.27 25 + 273.15 · (8.3163) Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Processes Marco Caniato Free University of Bozen Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Processes The differential form of the first law equation written for infinitesimal transformations and in specific terms gives − =U − m =U+P + ρ − = U + PV + H 2 2 + mgz + mgz When the fluid experiences negligible changes in its kinetic and potential energies Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Processes Passing to differential and unit of mass expressions − = u − = h = ! + "# !$ = −%!& + " !$ Only way to produce work in a close system is to move boundaries and thus to vary the volume. Only way to produce work in an open system is to move the flow inside the system. The volume will not vary and the motion is caused by pressure difference. Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Processes The equation can be used regardless the system is open or closed! % = RT ! +!%!& = "= − + %!& R "dT # dT ! + %!& = " dT − "# dT ! + "# dT = −%!& + " dT − = u = − = h Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Isobaric Processes The pressure is considerable constant during the process * = &!% + "# dT = −%!& + " dT P 1 * = −%!& + " dT = " 2 * * v1 v2 V = &!% = = −%!& = 0 $ − $, % − %, Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Isochoric Processes The volume is considerable constant during the process * = !% + "# dT = −%!& + " dT P * = !% + "# dT P1 1 * P2 2 * V = "# $ − $, = &!% = 0 = −%!& = −% & − &, Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Adiabatic Processes The heat transfer is null during the process − = u = ! + "# !$ − = −%!& + " !$ -$ !%.% 0 = ! + "# !$ 0 = -$ #⁄ # = h + -!$ ,⁄23, -!$ 1.0 − 1 " 0= "# Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Adiabatic Processes The heat transfer is null during the process !% 1 −$ = !$ % 0−1 !% 1 !$ − = % 0−1 $ !% 1 !$ 4 − = 4 % 0 − 1 , , $ Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Adiabatic Processes The heat transfer is null during the process %, 1 $ ln = ln % 0 − 1 $, Isothermic P 1 $ %, ln = ln % $, P1 P2 2 v1 v2 V %, = % $ $, , 23, , 23, Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Adiabatic Processes Other expression of adiabatic process %, = % $ $, , 23, , , $, 23, $ 23, $ = $ &, , & 2 2 1 23, 1 23, $ = $ &, , & , %, $,23, =% $ -$ % = & , 23, , , -$, 23, -$ 23, $, = $ &, & , , 1 23, 1 23, 7, 7, $ = $ &, , & 2 &,3, $,23, =& 2 3, 23, $ 2 &,3, $,23, 23, 2 = & 2 3, 23, $ 23, 2 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Adiabatic Processes Other expression of adiabatic process 2 &,3, $,23, ,32 &, 2 $, 23, 2 =& = & ,32 2 $ & $ = - 2 3, 23, $ 23, 2 ,32 &, 2 &, %, 23, 2 (3,) &, $, =& ,3272 &, 2 %, ,32 2 =& &% ,3272 2 % =& 23, 2 (3,) ,32 $, &, 2 $ ,32 2 7, &, %, , &,2 %, =& , 2 =& % ,32 2 7, =$ & ,32 2 % &, %,2 = & %2 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Polytropic Processes Polytrophic processes are generally considered to be a generalization of isothermal and adiabatic processes &v = cost isobaric n=0 isothermal n=1 isochoric n→∞ adiabatic n=k = ! + "# !$ − = h cannot be simplified Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 1 A tank with volume V=58 dm3 contains nitrogen (N2) at a pressure of 1.5 bar and at a pressure of temperature of 27°C. Nitrogen molecular mass is 28.01 and it is compressed up to 12 bar and the final volume occupied by gas is 10 dm3. The work carried out on the compression system is of 10 kJ. Determine the heat exchange and enthalpy variation. Ru is 8314 J / kg K compression Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 1 Enthalpy of nitrogen [kJ/kg] Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 1 ℎ = A + -$ SCHEME Q=? ∆H? = ℎ = A + · ∆A + W ∆A = A − A, &, , = - $, -EF = ℎ, = A, + % & tables = -G HEF -$ & $= - ℎD depends on temperature , %, ℎ, = A, + -$, Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 1 A tank with volume V=58 dm3 contains nitrogen (N2) at a pressure of 1.5 bar and at a pressure of temperature of 27°C. Nitrogen molar mass is 28.01 u and it is compressed up to 12 bar and the final volume occupied by gas is 10 dm3. The work carried out on the compression system is of 10 kJ. Determine the heat exchange and enthalpy variation. Ru is 8314 J / kg K -EF &, , = - $, 8314 O = = 296.8 28.01 0P Q &, , = - $, 1.5 · 10S · 0.058 = 296.8 · (27 + 273.15) = 0.098 0P Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 1 A tank with volume V=58 dm3 contains nitrogen (N2) at a pressure of 1.5 bar and at a pressure of temperature of 27°C. Nitrogen molar mass is 28.01 u and it is compressed up to 12 bar and the final volume occupied by gas is 10 dm3. The work carried out on the compression system is of 10 kJ. Determine the heat exchange and enthalpy variation. Ru is 8314 J / kg K & = -$ & $= - 12 · 10S · 0.01 = 414 Q = 296.8 · 0.098 The enthalpy and internal energy values of state 2 now can be inferred Interpolation on tables Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 1 Linear interpolation: WV − W, U − U, UV = + U, W − W, W, WV W U, UV U Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 1 Linear interpolation: UV,Y 520.4 − 415.7 414 − 400 = + 415.7 500 − 400 ℎ = 430.4 0O/0P A =? Linear interpolation h = u + Pv Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 1 A =ℎ −& % A = ℎ − -$ Volume per unit of mass not known Ideal gas law O A = 430.4 · 10 − 296.8 ∗ 414 = 307524.8 0P Q \ Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 1 − ^ = A − A, = A − A, + ^ = ∆_ = · 10 0O = 307.5 − 222.7 + − = −17.63 0.098 0P = 0.098 · −17.63 = −1.720O · (ℎ − ℎ, ) ∆_ = 0.098 · (430.4 − 311.8) = 11.6 0O Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 2 A closed system contains 3 kg of air. The system undergoes an adiabatic and reversible transformation from state 1 (P1=3 bar, T1=100°C) to state 2 (T2=300°C). Determine the pressure and volume at the end of the transformation, the changes in enthalpy and internal energy, the work exchanged P1 = 3 bar T1= 100 °C m= 3 kg Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 2 Enthalpy of air [kJ/kg] Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato ℎ = A + -$ Exercise 1 SCHEME ℎ = A + W=? ∆H? ∆U? = % · ∆A + W ∆A = A − A, ℎ, = A, + adiabatic V2? P2=? tables = -$ & , %, ,32 $, &, 2 ℎD depends on temperature ℎ, = A, + -$, = $& ,32 2 Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 2 ,32 $, &, 2 3 · 10 & S = = $& ,32 2 100 + 273.15 300 + 273.15 -$ ,32 $, &, 2 $ ,VVS `,a ,VVS ,3 `,a = =& ,32 2 2 &, $,,32 2 ,32 $ =& &, $, $ = 13.47 · 10S &b = & 3 · 287 · (300 + 273.15) -$ = 13.47 · 10S & = 0.37 \ 2 ,32 = Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 2 Linear interpolation: WV − W, U − U, UV = + U, W − W, W, WV W U, UV U Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 2 Linear interpolation: UV,Y, 401.8 − 300.6 373.5 − 300 = + 300.6 400 − 300 ℎ, = 374.6 0O/0P A =? A, =? ℎ = 580.6 0O/0P Linear interpolation h = u + Pv ∆_ = (ℎ − ℎ, ) ∆_ = 618 0O Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 2 A =ℎ −& % A = ℎ − -$ Volume per unit of mass not known A, = ℎ, − &, %, Ideal gas law A, = ℎ, − -$, Volume per unit of mass not known A = 416.10O/0P A, = 267.5 kJ/kg Ideal gas law Engineering thermodynamics and heat and mass transfer Prof. Marco Caniato Exercise 2 ∆e = ∆e = (A − A, )= 445.8 0O − −445.8 0O = compression Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Second Law of thermodynamics Marco Caniato Free University of Bozen Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Second law of thermodynamics It is common experience that a hot egg left in a cooler room eventually cools off Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Second law of thermodynamics It is clear from these arguments that processes proceed in a certain direction and not in the reverse direction ONE WAY Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Second law of thermodynamics In the development of the second law of thermodynamics, it is very convenient to have a hypothetical body with a relatively large thermal energy capacity (mass times specific heat) that can supply or absorb finite amounts of heat without undergoing any change in temperature. Such a body is called a thermal energy reservoir Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Second law of thermodynamics work can easily be converted to other forms of energy, but converting other forms of energy to work is not that easy. Win WQ outout Qin Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Second law of thermodynamics Heat engines differ considerably from one another, but all can be characterized by the following: 1. They receive heat from a high-temperature source (solar energy, oil furnace, nuclear reactor, etc.) 2. They convert part of this heat to work (usually in the form of a rotating shaft) 3. They reject the remaining waste heat to a low-temperature sink (the atmosphere, rivers, etc.). 4. They operate on a cycle. Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Second law of thermodynamics Heat engines and other cyclic devices usually involve a fluid to and from which heat is transferred while undergoing a cycle. This fluid is called the working fluid high temperature source Qin Heat engine Wout Win Wnet Qout Low temperature sink Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Second law of thermodynamics Thermal efficiency: Qout represents the magnitude of the energy wasted in order to complete the cycle. But Qout is never zero ℎ = η= η=1− ℎ , Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Second law of thermodynamics Kelvin-Plank Statement: It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work. Thermal energy reservoir Qin =100 KJ Heat engine Wnet =100 KJ Qout = 0 J Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Second law of thermodynamics Refrigerators and heat pumps. Refrigerators, like heat engines, are cyclic devices. The working fluid used in the refrigeration cycle is called a refrigerant. Warm environment TH>TL QH evaporator compressor engine condenser Required input Wnet QL Desired output Cold refrigerated space Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Second law of thermodynamics Performance. The efficiency of a refrigerator is expressed in terms of the coefficient of performance (COP). & ' "#$% = ( ) "#$% = , = & & + , * − + Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Acoustics 1 Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato What is Sound? 2 Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato What is Sound? 3 Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato What is Sound? 4 Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato What is Sound? R = 287 c0 λ= f c0 = ( J / kgK ) γ ⋅ R ⋅T γ = 1 . 41 T = t + 273 ( K ) 5 Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato What is Sound? Lp = 10 log p2/prif2 = 20 log p/prif (dB) Lv = 10 log v2/vrif2 = 20 log v/vrif LI = 10 log I/Irif Leq ,T 1 = 10 log T T 0 p 2 (t ) dt prif2 (dB) prif = 20 µPa (dB) vrif = 50 nm/s. Irif = 10-12 W/m2. Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Level sum: What is Sound? Lp1 = 10 log (p1/prif)2 (p1/prif)2 = 10 Lp1/10 Lp2 = 10 log (p2/prif)2 (p2/prif)2 = 10 Lp2/10 (pT/prif)2 = (p1/prif)2 + (p2/prif)2 = 10 Lp1/10 + 10 Lp2/10 LpT = Lp1 + Lp2 = 10 log (pT/prif)2 = 10 log (10 Lp1/10 + 10 Lp2/10 ) Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato What is Sound? • Example 1: L1 = 80 dB L2 = 85 dB LT= ? LT = 10 log (1080/10 + 1085/10) = 86.2 dB. • Example 2: L1 = 80 dB L2 = 80 dB LT = 10 log (1080/10 + 1080/10) = = 10 log (2* 10 80/10) = 10 log (2) + 10 log (10 80/10) = 10 log (2) + 10 * 80 / 10 = LT = 80 + 10 log 2 = 83 dB. Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato What is Sound? Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato What is Sound? Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato What is Sound? Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Sound insulation outside noise airborne noise Plant vibrations Impact noise 12 Sound insulation & Sound absorption absorption, reflection and transmission coefficients Energy balance equation for a wave impacting a surface: • Ei = Er + Ea + Et Ei = incident sound energy, Er = reflected sound energy Ea = absorbing sound energy (converted into heat) Et = transmitted sound energy Engineering Thermodynamics and Heat Transfer Prof. Marco Caniato Sound-absorbing systems are used for the acoustic treatment of rooms when it is necessary to reduce reverberated sound energy. Their use allows you to control the reverberation time parameter and the total sound pressure level in the room. The physical principle behind sound absorption is the conversion of part of the incident sound energy into heat 14 Sound insulation & Sound absorption Direct waves come from the source and reach the listener directly, as if he were in a free field. Reflected waves are produced by all reflections on the walls enclosing the room. The part of energy reflected from room surfaces depends on their acoustic behavior, in particular on the absorption, reflection and transmission coefficients (a,r and t). Sound insulation & Sound absorption Ea a= Ei Er r= Ei Difference between a sound-insulating and a sound-absorbing material: Sound insulating material: is useful to minimize the transmitted sound energy “Et”. Sound absorbing material: is useful to minimize the reflected sound energy “Er”. Et t= Ei Sound insulation & Sound absorption Ea a= Ei Er r= Ei Et t= Ei Apparent sound absorption coefficient Er α = 1− r = a + t = 1− Ei Sound Reduction Index Ei 1 R = 10 ⋅ log = 10 ⋅ log t Et t=0.01 (1 %) R=20 dB t=0.001 (0,1%) R=30 dB t=0.00001 (0,0001%) R=50 dB Sound Insulating Materials The “mass law” in acoustics is the base of air-borne sound insulation: Ei 1 R = 10 ⋅ log = 10 ⋅ log t Et • Stiffness Controlled Region: R drops by 6 dB/octave. •Resonant Frequencies (natural resonant frequencies specific of each panel). • Mass Controlled Region: R increases by 6 dB/octave. • Critical Frequency and Coincidence (the effect of coincidence reduces the sound insulation proprieties of the panel). Sound Insulating Materials Different structures have different “mass law” frequency behaviour: 1 2 Sound absorbing materials and structures Reverberation Time Er α = 1− r = a + t = 1− Ei Er r= Ei S’ S1 S Direct sound R S R Reflected sound (method of image sources) Sound absorbing materials and structures Reverberation Time L (dB) t [s] V = volume of the room [m3] TR = 0.16 ⋅ V (α ⋅ S ) i i i [s] Si = surface of i-element [m2] αi = apparent sound absorption coefficient of i-element A= α S equivalent absorption surface [m2] Sound absorbing materials and structures Sound level attenuation“∆L” in an enclosed space : ∆L (f) = 10 log (A2/ A1) A 1 = α1 S A 2 = α2 S (dB) equivalent absorption surface without sound absorbing elements [m2] equivalent absorption surface with sound absorbing elements [m2]. Sound absorbing materials and structures ISO 354:2003 specifies a method of measuring the sound absorption coefficient of acoustical materials used as wall or ceiling treatments, or the equivalent sound absorption area of objects, such as furniture, persons or space absorbers, in a reverberation room. Sound absorbing materials and structures Results of sound absorption coefficient of acoustical materials obtained in a reverberation room. Sound absorbing materials and structures ISO 10534-2:1998. Acoustics — Determination of sound absorption coefficient and impedance in impedance tubes (or Kundt tubes) 2 microphones loudspeaker Sound absorbing materials and structures What is the acoustic impedance of a material/surface? Sound absorbing materials and structures What is the acoustic impedance of a material/surface? Z0 = ρ0c0 represents the characteristic impedance of the fluid Sound absorbing materials and structures Depending on the different acoustic behaviour at different frequencies, sound-absorbing materials are generally classified into: a) porous materials, b) acoustic resonators c) vibrating panels, d) mixed systems. Sound absorbing materials and structures POROSITY: viscous friction F CAVITY AND MEMBRANE RESONANCE: damping of the oscillation M K Sound absorbing materials and structures POROUS MATERIALS open pore structure, including on the outer surface, and communicating with each other yes no pore size << λ complex geometric shapes that are difficult to describe with deterministic mathematical models with respect to sound propagation, the material seem as a homogeneous medium, in which viscous losses occur. are represented by average properties of: fibre diameter, porosity, structure factor, flow resistivity Sound absorbing materials and structures POROUS MATERIALS Fibre diameter: statistical distribution and mean value as a function of considered density Porosity: e = Vpore / Vtot good sound absorption if e>90-95%. Structure factor: influence of the geometric form of the material structure on the propagation of the sound wave. It is determined by specific acoustic measurements and it depends an the impedence values. Sound absorbing materials and structures POROUS MATERIALS R= ∆p Qv [Pa ⋅ s/m 3 ] Flow resistence ∆p [Pa ⋅ s/m] v Specific flow resistence Rs = R ⋅ A = Low flow resistivity High flow resistivity r= RS ∆p = d v⋅d [Pa ⋅ s/m 2 ] Flow resistivity (not dependent by the thickness) If the flow resistance is high, the sound waves cannot penetrate the material; if it is low, they do not encounter sufficient friction to dissipate the energy. Sound absorbing materials and structures POROUS MATERIALS Flow resistivity (EN 29053) Sound absorbing materials and structures POROUS MATERIALS Flow resistivity and Sound absorption Sound absorbing materials and structures POROUS MATERIALS analytical models for calculating the sound absorption properties of fibrous and porous materials • rock fibres • glass fibres • animal wools • vegetable fibers or wools • polyester fibres • open-cell polyurethane • foammelamine resins • felts • Etc Sound absorbing materials and structures POROUS MATERIALS Case a) Material placed on the wall >f>α > thick. > αlow freq. Sound absorbing materials and structures POROUS MATERIALS Case b) Material spaced from the wall near wall: Vair=0 • no friction • minimum absorption efficiency far from wall: Vair increase absorption efficiency increases Sound absorbing materials and structures POROUS MATERIALS Case b) Material spaced from the wall Vair,max and αmax when d=λ/4 The choice of porous material depends on: type of application; absorption; ease of processing; fire behaviour. Sound absorbing materials and structures POROUS MATERIALS Absorption coefficient measured in reverberation chamber of a glass fibre panel mounted at different distances from the wall Sound absorbing materials and structures POROUS MATERIALS REVERBERATION TIME No treatment With porous sound absorbing treatment Helmotz Resonator c f0 = 0 2π r2 π V l + 2r [Hz ]