Einstein Newton Experimental Physic 2 Dr. Tran Le Luu Master Program in Mechatronics and Sensor Systems Technology Vietnamese German University Content • • • • • Thermodynamics Electricity & Magnetic Oscillation & Mechanical wave Light & Optic Modern physics: Quantum mechanics, Nuclear structure Course Structure • • • Lecture Every Thursday 1 PM - 4:15 PM • Lecture materials will be made available before the lecture • Final Exams: June 2018 Tutorial (Tuesday 2:45 PM – 4:15 PM every 2 weeks from March 27th, 2018) • Opportunity for discussions on course material, problems and questions exam prep, etc. • Homework: is assigned to practice the material covered in this course and to enhance your analytical problem solving skills Laboratory: every 2 Monday 1 PM - 4:15 PM • Free fall • Heat capacity of metal • Moment of inertia and torsional vibrations • Force oscillator • Reversible pendulum • Stationary ultrasonic waves, determination of wavelength ► Must past the laboratory exam for final grade ► Must read the material before the experiment ► Hands-on experience with measurements and interpreting data Resources • Lecturer : Tran Le Luu (MSST Lecturer) Room 111B, office hours on weekday Email: email@example.com Phone number: 0968.913.909 • References * Serway/Jewett (2007): Physics for Scientists and Engineers with modern physics. 7th Ed. Thomson * Berkeley Physics Course (1965-1971). 5 volumes. McGraw-Hill * R.P. Feynman, R.B. Leighton, M.Sands (1964): The Feynman Lectures, Addison Wesley * Bohrmann, S.; Pitka, R.; Stöcker, H.; Terlecki, G. (2005): Physik für Ingenieure. Frankfurt/M: Harri Deutsch * Luong Duyen Binh, Vat Ly Dai Cuong, NXB Giao Duc Grading • Homework + participation + seminar: 10% • Final Exam: 40% • Grade: 1-5 • Pass: ≤ 4 Note: No credit for late homework Seminar Topic Principle, Operation & Application 1. Laser 2. X-ray 3. Scanning Electron Microscopy (SEM) 4. Transmission Electron Microscopy (TEM) 5. Atomic Force Microscopy (AFM) 6. Orbit - Planet 7. UV-VIS 8. Sensor 9. LED 10. Automation Chapter 8 Thermodynamic Thermal phenomena: temperature, heat, and internal energy Properties of Gases • The properties of a gas are almost independent of its identity (Gas molecules behave as if no other molecules are present) – Compressible – Low density – Expand to fill a container – Form homogeneous mixtures Example: Comparison of liquid and gaseous water 1 mole of water ~18 grams One mole liquid water occupies less than half the volume of a golf ball One mole of water vapor (20ºC, 1 atm) occupies more than the volume of 3 basketballs Gases Exert Pressure: What is Pressure? • Pressure is defined as the force exerted divided by the area it acts over • Pressure = Force/Area • Typical Units are lbs/in2 or kg/m2 • If a woman changes her shoes from sneakers to high heels does she exert a different pressure on the floor? • Where does the pressure that a gas exerts come from? • The mattress of a water bed is 2.00 m long by 2.00 m wide and 30.0 cm deep. (A) Find the weight of the water in the mattress. (B) Find the pressure exerted by the water on the floor when the water bed rests in its normal position. Assume the entire lower surface of the bed makes contact with the floor. Measuring Atmospheric Pressure • Barometer – device that measures atmospheric pressure – Invented by Evangelista Torricelli in 1643 Atmospheric Pressure – Changing weather conditions – Changing altitude Units of Pressure 1 standard atmosphere = 1.000 atm = 760.0 mm Hg = 760.0 torr = 101,325 Pa (1 Pa = 1 N/m2) If a weatherman says that atmospheric pressure is 29.12 inches of mercury, what is it in torr? • The mattress of a water bed is 2.00 m long by 2.00 m wide and 30.0 cm deep. (A) Find the weight of the water in the mattress. (B) Find the pressure exerted by the water on the floor when the water bed rests in its normal position. Assume the entire lower surface of the bed makes contact with the floor. What is the pressure (in atm) on a surface 20.0 ft under water, if the atmospheric pressure is 1.023 atm, and the densities of water and mercury are 1.00 and 13.6 g/mL, respectively? Solution: P = 1.023 atm 20 ft Pressure and Volume: Boyle’s Law Draw a graph of V vs. P and also V vs. 1/P Pressure and Volume: Boyle’s Law • Graphing Boyle’s results • This graph has the shape of half of a hyperbola with an equation PV = k or V = k/P • Volume and pressure are inversely proportional. – If one increases the other decreases. Pressure and Volume: Boyle’s Law Another way of stating Boyle’s Law is P1V1 = P2V2 (constant temperature and amount of gas) Volume and Moles: Avogadro’s Law • Volume and moles are directly proportional. – If one increases the other increases – constant temperature and pressure • Another way of stating Avogadro’s Law is V1 = V2 n1 n2 (constant temperature and pressure) The Gas Laws Ideal Gas Law pV=nRT R = universal gas constant= 8,314 J/(K mol) pv= R i = individual gas constant= Ri = R/M unit [J/(kg K)] Ri T • A spray can containing a propellant gas at twice atmospheric pressure (202 kPa) and having a volume of 125.00 cm3 is at 22°C. It is then tossed into an open fire. When the temperature of the gas in the can reaches 195°C, what is the pressure inside the can? Assume any change in the volume of the can is negligible For an ideal gas, calculate the pressure of the gas if 0.215 mol occupies 338 mL at 32.0ºC. A steel cylinder with a volume of 68.0 L contains O 2 at a pressure of 15,900 kPa at 23ºC. What is the volume of this gas at STP? Mixtures of Gases Thought experiment on ideal gas mixtures: • In gaseous mixtures, each gas behaves as though it occupies the container alone. – Assuming no reaction between gases Gas 1 V1, m 1, p, T p V 1 = m1 R 1 T p 1 V = m1 R 1T Gas 2 V2 , m2, p, T p V 2 = m2 R 2 T p 2 V = m2 R 2 T Gas 3 V3 , m3, p, T p V3 = m 3 R 3 T p 3 V = m 3 R 3T Partial pressure Total pressure p = p 1 + p2 + p 3 Mixtures of Gases Dalton´s Law: The total pressure exerted by a gaseous mixture is equal to the sum of the partial pressures of each Individual component. PN Ptotal = PN + PO 2 2 Add O2 2 Oxygen was produced and collected over water at 22ºC and a pressure of 754 torr. 2 KClO3(s) 2 KCl(s) + 3 O2(g) 325 mL of gas were collected and the vapor pressure of water at 22ºC is 21 torr. Calculate the number of moles of O2 and the mass of KClO3 decomposed. • Diffusion: the mixing of gases as a results of random motion and collisions. Open valve • Effusion: the escape of a gas from a container to a region of vacuum Real Gases An ideal gas is a theoretical gas composed of many randomly moving point particles that do not interact except when they collide elastically. Real Gases Real Gases Real Gas Law e.g. van der Waals equation (p + a(n2/v2 ) (V-nb) = nR T e.g. Redlich-Kwong equation p = RT/(Vm-b) - a/(T 1/2 Vm (Vm+b)) a = parameter representing attractions b = parameter representing repulsions Thermodynamics Thermodynamics is concerned with the transformation of energy Energy transformations – mostly involve heat and work movements. The starting point for thermodynamic considerations are the laws of thermodynamics: Zeroth law First law Second law Third law Thermodynamic equilibrium is an equivalence relation conservation of energy why do some things happen naturally, some not ? absolute zero temperature Introduction A process must satisfy the first law in order to occur. Satisfying the first law alone does not ensure that the process will take place. Second law is useful: provide means for predicting the direction of processes, establishing conditions for equilibrium, determining the best theoretical performance of cycles, engines and other devices. Important terms Examples: Closed System Examples: Open System Isolated system Isolated system – neither mass nor energy can cross the selected boundary Example (approximate): coffee in a closed, well-insulated thermos bottle Properties of a system Properties of a system is a measurable characteristic of a system that is in equilibrium. Properties may be intensive or extensive. Intensive – Are independent of the amount of mass: Temperature, Pressure, and Density. Extensive – varies directly with the mass: mass, volume, energy, enthalpy State, Equilibrium and Process State – a set of properties that describes the conditions of a system. Eg. Mass m, Temperature T, volume V Thermodynamic equilibrium system that maintains thermal, mechanical, phase and chemical equilibriums. State, Equilibrium and Process The prefix iso- is often used to designate a process for which a particular property remains constant. Isobaric process: A process during which the pressure P remains constant. Pressure is Constant (ΔP = 0) State, Equilibrium and Process Isochoric (or isometric) process: A process during which the specific volume v remains constant Isothermal process: A process during which the temperature T remains constant. . Process Property held constant isobaric pressure isothermal temperature isochoric volume isentropic entropy Types of Thermodynamics Processes Cyclic process - when a system in a given initial state goes through various processes and finally return to its initial state, the system has undergone a cyclic process or cycle. Reversible process - it is defined as a process that, once having take place it can be reversed. In doing so, it leaves no change in the system or boundary. Irreversible process - a process that cannot return both the system and surrounding to their original conditions Types of Thermodynamics Processes Adiabatic process - a process that has no heat transfer into or out of the system. It can be considered to be perfectly insulated. Isentropic process - a process where the entropy of the fluid remains constant. Polytropic process - when a gas undergoes a reversible process in which there is heat transfer, it is represented with a straight line, PVn = constant. Throttling process - a process in which there is no change in enthalpy, no work is done and the process is adiabatic. Adiabatic Process • Air at 20.0°C in the cylinder of a diesel engine is compressed from an initial pressure of 1.00 atm and volume of 800.0 cm3 to a volume of 60.0 cm 3. Assume air behaves as an ideal gas with γ = 1.40 and the compression is adiabatic. Find the final pressure and temperature of the air. What is Pure Substances? A substance that has a fixed chemical composition throughout is called a pure substance. A pure substance does not have to be of a single chemical element or compound, however. A mixture of various chemical elements or compounds also qualifies as a pure substance as long as the mixture is homogeneous. What is Pure Substances? A mixture of liquid and water vapor is a pure substance, but a mixture of liquid and gaseous air is not. Examples: Water (solid, liquid, and vapor phases) Mixture of liquid water and water vapor Carbon dioxide, CO2 Nitrogen, N2 Mixtures of gases, such as air, as long as there is no change of phase. Phases of A Pure Substance The substances exist in different phases, e.g. at room temperature and pressure, copper is solid and mercury is a liquid. It can exist in different phases under variations of condition. There are 3 Principal phases • solid • Liquid • gas Each with different molecular structures. Phase-change Processes of Pure Substances There are many practical situations where two phases of a pure substances coexist in equilibrium. E.g. water exists as a mixture of liquid and vapor in the boiler and etc. Solid: strong intermolecular bond Liquid: intermediate intermolecular bonds Gas: weak intermolecular bond Solid Liquid Gas Zeroth Law of Thermodynamics “ If two bodies are in thermal equilibrium with a third body, there are also in thermal equilibrium with each other.” Thermal equilibrium is a situation in which two objects would not exchange energy by heat or electromagnetic radiation if they were placed in thermal contact State Functions A state function depends only on the current state of a system The change in a state function between two states is independent of the path between them Internal energy is a state function; work and heat are not Heat is defined as the transfer of energy across the boundary of a system due to a temperature difference between the system and its surroundings The First Law Fundamental properties: Work and Energy Work is the transfer of energy to a system by a process that is equivalent to raising or lowering a weight: N.L.S. Carnot W = force X distance Total capacity to do work Internal Energy The internal energy of a system may be changed by doing work P.P. Joule ΔU =W The First Law Heat is energy transferred as a result of temperature difference. Energy flows as heat from a high temperature region to a low temperature region. Adiabatic systems do not allow heat to pass the system boundary doing work by heat but diathermic systems do allow. Example for adiabatic system: Dewar If the internal energy is changed only by heating: ΔU= Q The First Law The First Law of Thermodynamics: The internal energy of an isolated system is constant. Definition: Going out of the System: < 0 Going into the System: > 0 First Law The First Law is usually referred to as the Law of Conservation of Energy, i.e. energy can neither be created nor destroyed, but rather transformed from one state to another. The energy balance is maintained within the system being studied/defined boundary. The various energies associated are then being observed as they cross the boundaries of the system. Energy Balance for Closed System V Closed System Heat Work z Reference Plane, z = 0 or Ein Eout E system According to classical thermodynamics Qnet Wnet E system The total energy of the system, Esystem, is given as E = Internal energy + Kinetic energy + Potential energy E = U + KE + PE The change in stored energy for the system is E U KE PE The first law of thermodynamics for closed systems then can be written as Qnet Wnet U KE PE If the system does not move with a velocity and has no change in elevation, the conservation of energy equation is reduced to Qnet Wnet U The first law of thermodynamics can be in the form of qnet wnet 2 2 V2 V1 g ( z2 z1 ) u2 u1 2000 1000 (kJ / kg ) Q net W net 2 2 V2 V1 g ( z2 z1 ) m u2 u1 2000 1000 (kJ ) For a constant volume process, 2 2 V2 V1 g ( z2 z1 ) Q net W net m u2 u1 2000 1000 2 2 V2 V1 g ( z2 z1 ) Q net m u2 u1 2000 1000 For a constant pressure process, Q net W net 2 2 V2 V1 g ( z2 z1 ) m u2 u1 2000 1000 2 2 V2 V1 g ( z2 z1 ) Q net P(V2 V1 ) m u2 u1 2000 1000 Q net 2 2 V2 V1 g ( z2 z1 ) m u2 u1 P(V2 V1 ) 2000 1000 Q net 2 2 V2 V1 g ( z2 z1 ) m h2 h1 2000 1000 Example A closed system of mass 2 kg undergoes an adiabatic process. The work done on the system is 30 kJ. The velocity of the system changes from 3 m/s to 15 m/s. During the process, the elevation of the system increases 45 meters. Determine the change in internal energy of the system. Example Steam at 1100 kPa and 92 percent quality is heated in a rigid container until the pressure is 2000 kPa. For a mass of 0.05 kg, calculate the amount of heat supply (in kJ) and the total entropy change (in kJ/kg.K). Closed System First Law of a Cycle Some thermodynamic cycle composes of processes in which the working fluid undergoes a series of state changes such that the final and initial states are identical. For such system the change in internal energy of the working fluid is zero. The first law for a closed system operating in a thermodynamic cycle becomes Qnet Wnet U cycle Qnet Wnet The Molecular Origin of Internal Energy Internal energy is stored in a system as kinetic and potential energy. Contributions to kinetic energy: • Translation • Rotation • Vibration Equipartition Theorem: The average energy of each degree of freedom of a molecule is equal to ½ kT (1/2 RT per mol) Linear molecules: 5/2 kT; Nonlinear molecules: 3 kT (close to room temperature) Temperature dependency of c v,m (hydrogen gas) Measurement of Heat: Calorimetry Bomb calorimeter A common thermometer in everyday use consists of a mass of liquid— usually mercury or alcohol—that expands into a glass capillary tube when heated Thermal Expansion of Solid & Liquid • α Average coefficient of linear expansion • where β is the average coefficient of volume expansion • A segment of steel railroad track has a length of 30.000 m when the temperature is 0.0°C. (A) What is its length when the temperature is 40.0°C? (B) Suppose the ends of the rail are rigidly clamped at 0.0°C so that expansion is prevented. What is the thermal stress set up in the rail if its temperature is raised to 40.0°C? Enthalpy If there is no change in the volume of a system and no nonexpansion work is done o change in internal energy is equal to the energy supplied by heat: ΔU = Q at constant volume State function which is related to energy changes at constant pressure is called enthalpy: H = U + pV ΔH = ΔU + pΔV (+VΔp = 0) ΔH = Q + W + pΔV ΔH = Q - p exΔV + pΔV ΔH = Q at constant pressure Enthalpy The enthalpy of a system, state property, is a measure of the energy of a system that is available as heat at constant pressure. For an endothermic process, ΔH > 0; for an exothermic process, ΔH < 0 Heat Capacity The heat capacity of a substance is a measure of the temperature rise that occurs when the substance is heated. c = q/ΔT 4.18 J of mechanical energy raises the temperature of 1 g of water by 1°C Two cases: Heating at constant pressure and at constant volume. c p = Δh/ΔT and c v = Δu/ΔT For ideal gases: c p = c v + nR (molar: c pm= c vm + R) For linear molecules: c vm = 5/2 R, nonlinear molecules c vm = 3 R • A 0.050 0-kg ingot of metal is heated to 200.0°C and then dropped into a calorimeter containing 0.400 kg of water initially at 20.0°C. The final equilibrium temperature of the mixed system is 22.4°C. Find the specific heat of the metal. • A cylinder contains 3.00 mol of helium gas at a temperature of 300 K. (A) If the gas is heated at constant volume, how much energy must be transferred by heat to the gas for its temperature to increase to 500 K? (B) How much energy must be transferred by heat to the gas at constant pressure to raise the temperature to 500 K? • What mass of steam initially at 130°C is needed to warm 200 g of water in a 100-g glass container from 20.0°C to 50.0°C? • A 1.0-mol sample of an ideal gas is kept at 0.0°C during an expansion from 3.0 L to 10.0 L. (A) How much work is done on the gas during the expansion? (B) How much energy transfer by heat occurs between the gas and its surroundings in this process? (C) If the gas is returned to the original volume by means of an isobaric process, how much work is done on the gas? • A 1.0-kg bar of copper is heated at atmospheric pressure so that its temperature increases from 20°C to 50°C. (A) What is the work done on the copper bar by the surrounding atmosphere (B) How much energy is transferred to the copper bar by heat? (C) What is the increase in internal energy of the copper bar? • A student eats a dinner rated at 2 000 Calories. He wishes to do an equivalent amount of work in the gymnasium by lifting a 50.0-kg barbell. How many times must he raise the barbell to expend this much energy? Assume he raises the barbell 2.00 m each time he lifts it and he regains no energy when he lowers the barbell. Thermal Conduction • The process of energy transfer by heat can also be called conduction or thermal conduction • In this process, the transfer can be represented on an atomic scale as an exchange of kinetic energy between microscopic particles-molecules, atoms, and free electrons—in which less-energetic particles gain energy in collisions with more energetic particles Reaction Enthalpy The reaction enthalpy ΔH is the change in enthalpy per mole of substance as expressed by the stoichiometric numbers in the chemical equation. Example for thermochemical equation: CH4(g) + 2 O2(g) CO2 (g) + 2 H 2O(g) ΔH = -802 kJ The standard reaction enthalpy 'H° is the reaction enthalpy when reactants in their standard states change to products in their standard states (25°C, 1 bar). CH4(g) + 2 O2(g) CO2 (g) + 2 H 2O(l) ΔH° = -890 kJ The overall reaction enthalpy is the sum of the reaction enthalpies of the steps into which the reaction can be divided. Standard Enthalpy The standard enthalpy of formation ΔH f° of a substance is the standard reaction enthalpy for the formation of a substance from ist elements in their most stable form. Example: 2 C(s) + 3 H2 (g) + ½ O2(g) C 2H5OH(l) ΔH f °= -277.69 kJ mol-1 Standard enthalpies of formation can be combined to obtain the standard enthalpy of any reaction. ΔHr ° = ΣnΔH f °(products) - ΣnΔH f°(reactants) A cup of hot coffee does not get hotter in a cooler room. Transferring heat to a paddle wheel will not cause it to rotate. Transferring heat to a wire will not generate electricity. These processes cannot occur even though they are not in violation of the first law. Second Law of Thermodynamics Kelvin-Planck statement No heat engine can have a thermal efficiency 100 percent. As for a power plant to operate, the working fluid must exchange heat with the environment as well as the furnace. Heat Engines Work can easily be converted to other forms of energy, but? Heat engine differ considerably from one another, but all can be characterized : o they receive heat from a high-temperature source o they convert part of this heat to work o they reject the remaining waste heat to a lowtemperature sink atmosphere o they operate on a cycle The work-producing device that best fit into the definition of a heat engine is the steam power plant, which is an external combustion engine. Thermal Efficiency Represent the magnitude of the energy wasted in order to complete the cycle. A measure of the performance that is called the thermal efficiency. Can be expressed in terms of the desired output and the required input Desired Result th Required Input For a heat engine the desired result is the net work done and the input is the heat supplied to make the cycle operate. The thermal efficiency is always less than 1 or less than 100 percent. th Wnet , out Qin where Wnet , out Wout Win Qin Qnet Applying the first law to the cyclic heat engine Qnet , in Wnet , out U Wnet , out Qnet , in Wnet , out Qin Qout The cycle thermal efficiency may be written as th Wnet , out Qin Qin Qout Qin Qout 1 Qin A thermodynamic temperature scale related to the heat transfers between a reversible device and the high and lowtemperature reservoirs by QL TL QH TH The heat engine that operates on the reversible Carnot cycle is called the Carnot Heat Engine in which its efficiency is th , rev TL 1 TH • An engine transfers 2.00 103 J of energy from a hot reservoir during a cycle and transfers 1.50 103 J as exhaust to a cold reservoir. (A) Find the efficiency of the engine. (B) How much work does this engine do in one cycle? • A certain refrigerator has a COP of 5.00. When the refrigerator is running, its power input is 500 W. A sample of water of mass 500 g and temperature 20.0°C is placed in the freezer compartment. How long does it take to freeze the water to ice at 0°C? Assume all other parts of the refrigerator stay at the same temperature and there is no leakage of energy from the exterior, so the operation of the refrigerator results only in energy being extracted from the water. The Second Law There are many ways of stating the Second Law of thermodynamics: • In an isolated system, a process can occur only if it increases the total entropy S of the system. • It is impossible to convert heat completely into work. Entropy is a measure of disorder! ΔS = Q rev /T Q = n c dT dS = n c dT/T ΔS = n c lnT2/T1 increase in T increase in S The Second Law Change of S under isothermal expansion: W = -nRT lnV2/V1 ΔS = -W/T = nR ln V2 /V1 increase in V increase in S ΔS = nR ln p 1/p2 increase in pressure decrease in S Entropy increases when a solid melts to a liquid and when a liquid vaporizes more disorder! Many standard entropies are close to 85 J/(K mol) Trouton´s constant • The total entropy of an isolated system that undergoes a change cannot decrease. • If the process is irreversible, the total entropy of an isolated system always increases. In a reversible process, the total entropy of an isolated system remains constant. • Entropy Change in Thermal Conduction • Entropy Change in a Free Expansion • Let’s verify that the macroscopic and microscopic approaches to the calculation of entropy lead to the same conclusion for the adiabatic free expansion of an ideal gas. Suppose an ideal gas expands to four times its initial volume. As we have seen for this process, the initial and final temperatures are the same. (A) Using a macroscopic approach, calculate the entropy change for the gas. (B) Using statistical considerations, calculate the change in entropy for the gas and show that it agrees with the answer you obtained in part (A). The Second Law The standard reaction entropy is the difference in standard molar entropies of products and reactants, taking into account their stoichiometric coefficients: ΔSr° = ΣnΔS f°(products) - ΣnΔS f °(reactants) The standard reaction entropy is positive (increase in entropy) if there is a net production of gas in a reaction; it is negative (a decrease) if there is a net consumption of gas. Equilibrium When a system is at equilibrium, it has no tendency to change in either direction and will remain in its state until it is disturbed from outside the system. Examples: • Thermal equilibrium • Mechanical equilibrium • Physical equilibrium • Chemical equilibrium The criterion for equilibrium in thermodynamics is: ΔStot = 0 Free Energy This state function helps to judge whether a reaction is spontaneous. This can be carried out in one step, using a single table of data. ΔStot= ΔS sys + ΔS surr Process at T = const. and p = const. ΔS tot= ΔS sys - ΔH/T Introduction of the Gibbs energy: * -T ΔG = ΔH – TΔS (= -TΔS tot) Josiah Willard Gibbs 1839-1903 Free Energy At constant pressure and temperature, the direction of spontaneous change is the direction of decreasing free energy. Equilibrium condition: ΔG = 0 The Second Law The reaction free energy ΔGr is used as criterion of spontaneity for a chemical reaction. The standard reaction free energy is the difference of the standard molar free energies of the products and of the reactants: ΔGr° = ΣnΔGm°(products) - ΣnΔGm°(reactants) The standard free energy of formation ΔGf° of a compound is a measure of its stability relative to its elements! ΔGr° < 0; compound has a lower free energy than it elements elements have a spontaneous tendency to form the compound ΔGr° > 0 ; the decomposition of the compound is spontaneous The Second Law Standard Free Energies of Formation at 25°C Substance Gases ammonia NH3 Carbondioxide CO2 Nitrogendioxide NO 2 Liquids Water Benzene Solids calcium carbonate silver chloride ΔGf°[kJ/mol] -16.45 -394.4 +51.3 -237.1 +124.3 ___________ -1128.8 -109.8 The thermal efficiencies of actual and reversible heat engines operating between the same temperature limits compare as follows The coefficients of performance of actual and reversible refrigerators operating between the same temperature limits compare as follows Homework • • • • • 1. Liquid nitrogen has a boiling point of –195.81°C at atmospheric pressure. Express this temperature (a) in degrees Fahrenheit and (b) in kelvins. 2. In a student experiment, a constant-volume gas thermometer is calibrated in dry ice (–78.5°C) and in boiling ethyl alcohol (78.0°C). The separate pressures are 0.900 atm and 1.635 atm. (a) What value of absolute zero in degrees Celsius does the calibration yield? What pressures would be found at the (b) freezing and (c) boiling points of water? Hint: Use the linear relationship P = A + BT, where A and B are constants. 3. A copper telephone wire has essentially no sag between poles 35.0 m apart on a winter day when the temperature is −20.0°C. How much longer is the wire on a summer day when the temperature is 35.0°C? 4. The active element of a certain laser is made of a glass rod 30.0 cm long and 1.50 cm in diameter. Assume the average coefficient of linear expansion of the glass is equal to 9.00 × 10−6 (°C)−1. If the temperature of the rod increases by 65.0°C, what is the increase in (a) its length, (b) its diameter, and (c) its volume? 5. A volumetric flask made of Pyrex is calibrated at 20.0°C. It is filled to the 100-mL mark with 35.0°C acetone. After the flask is filled, the acetone cools and the flask warms, so that the combination of acetone and flask reaches a uniform temperature of 32.0°C. The combination is then cooled back to 20.0°C. (a) What is the volume of the acetone when it cools to 20.0°C? (b) At the temperature of 32.0°C, does the level of acetone lie above or below the 100-mL mark on the flask? Explain. • • • • 6. An auditorium has dimensions 10.0 m × 20.0 m × 30.0 m. How many molecules of air fill the auditorium at 20.0°C and a pressure of 101 kPa (1.00 atm)? 7. The pressure gauge on a tank registers the gauge pressure, which is the difference between the interior pressure and exterior pressure. When the tank is full of oxygen (O2), it contains 12.0 kg of the gas at a gauge pressure of 40.0 atm. Determine the mass of oxygen that has been withdrawn from the tank when the pressure reading is 25.0 atm. Assume that the temperature of the tank remains constant. 8. An automobile tire is inflated with air originally at 10.0°C and normal atmospheric pressure. During the process, the air is compressed to 28.0% of its original volume and the temperature is increased to 40.0°C. (a) What is the tire pressure? (b) After the car is driven at high speed, the tire’s air temperature rises to 85.0°C and the tire’s interior volume increases by 2.00%. What is the new tire pressure (absolute)? 9. The mass of a hot-air balloon and its cargo (not including the air inside) is 200 kg. The air outside is at 10.0°C and 101 kPa. The volume of the balloon is 400 m3. To what temperature must the air in the balloon be warmed before the balloon will lift off? (Air density at 10.0°C is 1.244 kg/m3.) • • • • • • 10. The highest waterfall in the world is the Salto Angel Falls in Venezuela. Its longest single falls has a height of 807 m. If water at the top of the falls is at 15.0°C, what is the maximum temperature of the water at the bottom of the falls? Assume all of the kinetic energy of the water as it reaches the bottom goes into raising its temperature. 11. The temperature of a silver bar rises by 10.0°C when it absorbs 1.23 kJ of energy by heat. The mass of the bar is 525 g. Determine the specific heat of silver from these data. 12. A 1.50-kg iron horseshoe initially at 600°C is dropped into a bucket containing 20.0 kg of water at 25.0°C. What is the final temperature of the water-horseshoe system? Ignore the heat capacity of the container and assume a negligible amount of water boils away 13. A 3.00-g lead bullet at 30.0°C is fi red at a speed of 240 ms into a large block of ice at 0°C, in which it becomes embedded. What quantity of ice melts? 14. In an insulated vessel, 250 g of ice at 0°C is added to 600 g of water at 18.0°C. (a) What is the final temperature of the system? (b) How much ice remains when the system reaches equilibrium? 15. An ideal gas is enclosed in a cylinder with a movable piston on top of it. The piston has a mass of 8 000 g and an area of 5.00 cm2 and is free to slide up and down, keeping the pressure of the gas constant. How much work is done on the gas as the temperature of 0.200 mol of the gas is raised from 20.0°C to 300°C? • • • • • • • 16. A thermodynamic system undergoes a process in which its internal energy decreases by 500 J. Over the same time interval, 220 J of work is done on the system. Find the energy transferred from it by heat. 17. An ideal gas initially at 300 K undergoes an isobaric expansion at 2.50 kPa. If the volume increases from 1.00 m3 to 3.00 m3 and 12.5 kJ is transferred to the gas by heat, what are (a) the change in its internal energy and (b) its final temperature? 18. (a) How much work is done on the steam when 1.00 mol of water at 100°C boils and becomes 1.00 mol of steam at 100°C at 1.00 atm pressure? Assume the steam to behave as an ideal gas. (b) Determine the change in internal energy of the system of the water and steam as the water vaporizes. 19. A 2.00-mol sample of helium gas initially at 300 K and 0.400 atm is compressed isothermally to 1.20 atm. Noting that the helium behaves as an ideal gas, find (a) the final volume of the gas, (b) the work done on the gas, and (c) the energy transferred by heat. 20. Calculate the mass of an atom of (a) helium, (b) iron, and (c) lead. Give your answers in kilograms. The atomic masses of these atoms are 4.00 u, 55.9 u, and 207 u, respectively. 21. In an ultrahigh vacuum system (with typical pressures lower than 10 −7 pascal), the pressure is measured to be 1.00 × 10−10 torr (where 1 torr = 133 Pa). Assuming the temperature is 300 K, find the number of molecules in a volume of 1.00 m3. 22. (a) How many atoms of helium gas fill a spherical balloon of diameter 30.0 cm at 20.0°C and 1.00 atm? (b) What is the average kinetic energy of the helium atoms? (c) What is the rms speed of the helium atoms? • • • • • • 23. A 1.00-mol sample of hydrogen gas is warmed at constant pressure from 300 K to 420 K. Calculate (a) the energy transferred to the gas by heat, (b) the increase in its internal energy, and (c) the work done on the gas. 24. A 2.00-mol sample of a diatomic ideal gas expands slowly and adiabatically from a pressure of 5.00 atm and a volume of 12.0 L to a final volume of 30.0 L. (a) What is the final pressure of the gas? (b) What are the initial and final temperatures? Find (c) Q, (d) Δeint and (e) W for the gas during this process. 25. A particular heat engine has a mechanical power output of 5.00 kW and an efficiency of 25.0%. The engine expels 8.00 × 103 J of exhaust energy in each cycle. Find (a) the energy taken in during each cycle and (b) the time interval for each cycle. 26. One of the most efficient heat engines ever built is a coal-fired steam turbine in the Ohio River valley, operating between 1870°C and 430°C. (a) What is its maximum theoretical efficiency? (b) The actual efficiency of the engine is 42.0%. How much mechanical power does the engine deliver if it absorbs 1.40 × 105 J of energy each second from its hot reservoir? 27. An ideal gas is taken through a Carnot cycle. The isothermal expansion occurs at 250°C, and the isothermal compression takes place at 50.0°C. The gas takes in 1.20 × 103 J of energy from the hot reservoir during the isothermal expansion. Find (a) the energy expelled to the cold reservoir in each cycle and (b) the net work done by the gas in each cycle. 28. In a cylinder of an automobile engine, immediately after combustion, the gas is confined to a volume of 50.0 cm3 and has an initial pressure of 3.00 × 106 Pa. The piston moves outward to a final volume of 300 cm3, and the gas expands without energy transfer by heat. (a) If γ = 1.40 for the gas, what is the final pressure? (b) How much work is done by the gas in expanding?