The First Law of Thermodynamics
Chemical Engineering Thermodynamics
Lecture No. 4
Engr. John Andrew A. Tiria, Ch.E, MSc.
Department Head, ChE
The First Law of Thermodynamics
Also, known as the Energy Conservation Principle
The first law of thermodynamics states that while energy
can be changed from one form to another, the total
quantity of energy, in the universe is constant.
∆𝐸𝑢𝑛𝑖𝑣 = 𝑜
SURROUNDING
+Τ−
𝑄
System
+Τ−
𝑊
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The first law by saying that the energy change of
the system must be equal to the energy
transferred across its boundaries from the
surroundings.
BOUNDARY
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Forms of Energy
Macroscopic forms = The macroscopic forms of energy are those a system possesses as a whole
with respect to some outside reference frame, such as kinetic and potential energies.
Also, is related to motion and the influence of some
external effects such as gravity, magnetism, electricity,
and surface tension.
𝑃𝐸 = 𝑚𝑔ℎ
1
𝐾𝐸 = 𝑚𝑣 2
2
Δ𝐸 = ∆𝑃𝐸 + ∆𝑘𝐸
The macroscopic energy of an object
changes with velocity and elevation.
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Forms of Energy
• MICROSCOPIC FORM-The microscopic forms of energy are those related to the molecular
structure of a system and the degree of the molecular activity, and they are independent of outside reference
frames. The sum of all the microscopic forms of energy is called the internal energy of a system and is
denoted by U.
Energy = Thomas Young (1807)
Energy in Thermodynamics – Lord Kelvin (1852)
Internal Energy (U) – Rudolph Clausius and William Rankine
Inner work, internal , Internal work, Intrinsic Energy
The internal energy of a substance does not include energy that it may possess as
a result of its gross position or movement as a whole. Rather it refers to energy of
the molecules comprising the substance.
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The First Law and other Basic Concepts
THE JOULE’S EXPERIMENT
• Joule’s experiment (1840 – 1849) to investigate
the equivalence of heat and work. The
Quantitative Relationship of Heat And Work.
• Prior to Joule, heat was considered to be a
invisible fluid known as caloric and flows from a
body of higher caloric to one with a lower caloric.
• Caloric theory of heat
• Joule’s experiment laid the foundation of the first
law of thermodynamics.
http://www.engineeringexpert.net/Engineering-ExpertWitness-Blog/james-prescott-joule-and-the-joule-apparatus
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Internal Energy
1. Changes in temperature, for example
𝑇𝑙𝑜𝑤 → 𝑇ℎ𝑖𝑔ℎ
(Sensible Heat)
2. Changes in phase, for example,
solid →gas
(Latent Heat)
3. Changes in chemical structure, that is,
chemical reaction (𝑁2 + 3𝐻2 → 2𝑁𝐻3 )
The internal energy of a system is the
The various forms of microscopic
sum of all forms of the microscopic
energies that make up sensible energy.
energies.
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First Law of Thermodynamics
𝑢𝑖𝑑𝑒𝑎𝑙 𝑔𝑎𝑠 = 𝑓(𝑇 𝑜𝑛𝑙𝑦)
7
Internal Energy
𝑢𝑖𝑑𝑒𝑎𝑙 𝑔𝑎𝑠 = 𝑓(𝑇 𝑜𝑛𝑙𝑦)
𝑢𝑟𝑒𝑎𝑙 𝑔𝑎𝑠 = 𝑢 𝑇, 𝑣
𝑜𝑟
𝑢𝑟𝑒𝑎𝑙 𝑔𝑎𝑠 = 𝑢 𝑇, 𝑃
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Sample Problem
1. If a large stone is dropped from a cliff 10 m high, how fast will it be going when it
hits the ground?
2. In Example 1, we considered the potential energy of a stone at the top of a 10-m
cliff. When it fell, it gained kinetic energy, resulting in a velocity around 31 miles/hr.
Consider now an equivalent mass of water initially at 25ºC. How hot would the
water end up if its internal energy increased by the same amount?
The temperature of the water barely changes! Thus the energy stored in a stone 10 m up a
cliff corresponds to a negligible amount of internal energy. This example illustrates that a large
amount of energy is stored in u relative to the other forms of energy, and, consequently, why we
are so interested in internal energy. As engineers, it provides us a large resource to be harvested.
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Review
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Review: Thermodynamic System
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THE ENERGY EQUATION
𝐸 = 𝑚𝑒 = 𝑈 + 𝐾𝐸 + 𝑃𝐸
= 𝑚(𝑢 + 𝑘𝑒 + 𝑝𝑒)
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3. A tank containing a fluid is stirred by a
paddle wheel. The work input to the paddle
wheel is 5090 kJ. The heat transfer from the
tank is 1500 kJ. Consider the tank and the
fluid inside a control surface and determine
the change in internal energy of this control
mass.
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Work and Heat
• The first law of thermodynamics states that energy cannot be created
or destroyed, only transformed from one form to another. Work and
heat are two ways in which energy can be transferred between
systems. Work is done when a force acts on an object and causes it to
move, while heat is the transfer of thermal energy between two
objects at different temperatures.
𝑊ሶ 𝑛𝑒𝑡
𝑄ሶ 𝑛𝑒𝑡
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• In thermodynamics, work and heat are both measured in joules, the
same unit used to measure energy. However, they are fundamentally
different in nature. Work is a mechanical process that involves the
movement of objects, while heat is a form of energy that moves from
hotter to cooler objects. Understanding the relationship between
work and heat is essential for understanding the behavior of energy in
physical systems.
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WORK
The classical definition of work is mechanical
work defined as a force F acting through a
displacement x, so incrementally
𝛿𝑊 = 𝐹𝑑𝑥
PV work
𝐹𝐸
𝑊= න
. 𝑑 𝐴𝑥 = න 𝑃𝐸 . 𝑑𝑉 = න 𝑃𝐸 𝑑𝑉 𝑐𝑜𝑠𝜃 = − න 𝑃𝐸 𝑑𝑉
𝐴
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4. Consider the constant pressure expansion that is
illustrated in Figure 4. Initially the system contains 1
mole of gas A at 2 bar within a volume of 10 L. The
expansion process is initiated by releasing the latch.
The gas in the cylinder expands until the pressure of
the gas matches the pressure of the surroundings. The
final volume is 15.2 L. Calculate work done by the
system during this process.
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Figure 4.
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Seatwork
Consider a stone having a mass of 10 kg and a
bucket containing 100 kg of liquid water. Initially
the stone is 10.2 m above the water, and the stone
and the water are at the same temperature, state 1.
The stone then falls into the water. Determine U,
KE, PE, Q, and W for the following changes of
state, assuming standard gravitational acceleration
of 9.806 65 m/s2.
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Review
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Work at Moving Boundaries
𝛿𝑊 = 𝐹𝑒𝑥𝑡 𝑑𝐿 = 𝑃𝑒𝑥𝑡 𝑑𝑉
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Slightly different piston/cylinder arrangement
2
1 𝑊2 = න 𝑃𝑑𝑉 = 𝐴𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑡ℎ𝑒 𝑝𝑟𝑜𝑐𝑒𝑠𝑠 𝑐𝑢𝑟𝑣𝑒
1
1
𝑃1 + 𝑃2 (𝑉2 − 𝑉2 )
1 𝑊2 =
2
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Shaft Work
Energy transmission with a rotating shaft is very common in
engineering practice Often the torque T applied to the shaft is
constant, which means that the force F applied is also constant.
For a specified constant torque, the work done during n
revolutions is determined as follows: A force F acting through a
moment arm r generates a torque T
This force acts through a distance s, which is related to the radius r by
Then the shaft work is determined from
ሶ
𝒘ሶ 𝒔 = 𝟐𝝅𝒏𝑻
where n is the number of revolutions per unit time.
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POLYTROPIC PROCESS
𝑃𝑉 𝑛 = 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡
Where n is not equal to 1
The polytropic exponent n is indicative of the type of process, and it can vary from minus to plus infinity.
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POLYTROPIC PROCESS
Where n = 1,
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5. A piston/cylinder assembly contains 2 kg
of liquid water at 20◦C and 300 kPa, as
shown in slide 22. There is a linear spring
mounted on the piston such that when the
water is heated, the pressure reaches 3 MPa
3
with a volume of 0.1 𝑚 .
a. Find the final temperature.
b. Plot the process in a P–v diagram.
c. Find the work in the process.
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6.
Air
in
a
spring-loaded
piston/cylinder setup has a pressure
that is linear with volume, P = A +
BV. With an initial state of P = 150
kPa, V = 1 L and a final state of 800
kPa, V = 1.5 L. Find the work done
by the air.
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SW
7. A nitrogen gas goes through a
polytropic process with n = 1.3 in a
piston/cylinder. It starts out at 600 K,
600 kPa and ends at 800 K. Is the
work positive, negative, or zero?
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HEAT
Conduction
Convection
Radiation
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8. Consider the constant transfer of
energy from a warm room at 20◦C
inside a house to the colder ambient
temperature of −10◦C through a
single-pane window.
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Reversible Processes
A process is reversible if, after the process occurs,
the system can be returned to its original state
without any net effect on the surroundings. This
result occurs only when the driving force is
infinitesimally small.
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Irreversible Process
Real processes are not reversible. They have
friction and are carried out with finite driving
forces. Such processes are irreversible
processes. In an irreversible process, if the
system is returned to its original state, the
surroundings must be altered.
𝑊𝐼𝑟𝑟 ≪ 𝑊𝑟𝑒𝑣
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Efficiency
𝑊𝑟𝑒𝑣
𝜂=
𝑊𝑖𝑟𝑟
One strategy for actual, irreversible processes is to
solve the problem for the idealized, reversible process
and then correct for the irreversibilities using an
assigned efficiency factor.
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Thermodynamic Property
• Internal Energy
𝑈= 𝑈𝑙𝑖𝑞 + 𝑈𝑣𝑎𝑝
• Enthalpy
H= U+PV
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Sample Problem
Find the phase and the missing properties of P,
T , v, u and X for water at
𝑜
a.500kpa, 100 𝐶
b.5000kpa, u =800kj/kg
3
c.5000kpa, v = 0.06 𝑚 /kg
𝑜
3
d.−6 𝐶, v = 1 𝑚 /kg
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•A piston/cylinder contains water with quality
75% at 200 kPa. Slow expansion is
performed while there is heat transfer and
the water is at constant pressure. The process
stops when the volume has doubled. How do
you determine the final state and the heat
transfer?
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First Law of thermodynamics for Closed System
The change of energy
∆ = Final − Initial
Illustration of closed system and sign conventions for
heat and work. All three forms of energy are considered.
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First Law of thermodynamics for Open System
𝑑𝑚
𝑚ሶ 𝑖𝑛 − ෍ 𝑚ሶ 𝑜𝑢𝑡
( )𝑠𝑦𝑠 = ෍
𝑖𝑛
𝑜𝑢𝑡
𝑑𝑡
𝐴𝑉
𝑚ሶ =
𝜈Ƹ
Schematic of an open system with two streams in and two
streams out. The piston shown in the plot is hypothetical; it
illustrates the point that flow work is always associated with
fluid flowing into or out of the system.
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Flow Work
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Equation for open system
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Enthalpy
ℎ = 𝑢 + 𝑝𝑣
Enthalpy provides us a property that is a convenient way to account for these
two contributions of flowing streams to the energy in open systems.
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Steady-State Energy Balances
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Unsteady-State Energy Balances
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Transient Form of Energy
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10. (Closed System)
Consider a piston–cylinder assembly containing 10.0 kg
of water. Initially, the gas has a pressure of 20.0 bar and
occupies a volume of 1.0 m3. The system undergoes a
reversible process in which it is compressed to 100 bar.
The pressure volume relationship during this process is
given by:
𝑃𝑉 1.5 = 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡
(a) What is the initial temperature?
(b) Calculate the work done during this process.
(c) Calculate the heat transferred during this process.
(d) What is the final temperature?
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11. Steam enters a turbine with a mass flow rate
of 10 kg/s. The inlet pressure is 100 bar and the
inlet temperature is 500ºC. The outlet contains
saturated steam at 1 bar. At steady-state,
calculate the power (in kW) generated by the
turbine.
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Thermochemical Data for U and H
Heat Capacity: 𝑪𝒗 𝒂𝒏𝒅 𝑪 𝒑
𝑯𝒆𝒂𝒕 𝒄𝒂𝒑𝒂𝒄𝒊𝒕𝒚 𝒂𝒕 𝑪𝒐𝒏𝒔𝒕𝒂𝒏𝒕 𝑽𝒐𝒍𝒖𝒎𝒆𝒏, 𝑪𝒗
∆𝒖 = 𝒒 closed system, constant V
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Heat Capacity at constant Pressure, Cp
∆𝒖 = 𝒒 + 𝒘 = 𝒒 − 𝑷∆𝒗
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The Mean heat Capacity
• For many gases, heat capacity data are often reported in
terms of the mean heat capacity
∆ℎ = 𝑐𝑃 (𝑇 − 298)
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Latent Heat
When a substance undergoes a phase change, there is a substantial change in internal energy associated with
it
• Enthalpy of Vaporization
• Enthalpy of Fusion
• Enthalpy of Sublimation
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Enthalpy of Reaction
• A large amount of energy is “stored” in the chemical
bonds within molecules. When the atoms in
molecules rearrange by undergoing a chemical
reaction, the energy stored within the bonds of the
products is typically different from that of the
reactants. Thus, significant amounts of energy can be
absorbed or liberated during chemical reactions.
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Consider heating 2 moles of steam from 200ºC and 1
MPa to 500ºC and 1 MPa. Calculate the heat input
required using the following sources for data:
(a)Heat Capacity
(b)Steam tables
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Use the data available in Appendix to calculate the mean heat
capacity, cp, for air between T1 = 298 K and T2 = 300 to 1000
K, in intervals of 100 K.
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•You need to preheat a stream of air flowing
steadily at 10 mol/min from 600 K to 900 K.
Determine the heat rate required using the
mean heat capacity data from previous Example.
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10 mol/sec of liquid hexane flows into a steady-state boiler at 25ºC. It
exits as a vapor at 100ºC. What is the required heat input to the
heater? Take the enthalpy of vaporization at 68.8ºC to be:
𝑘𝑗
∆ℎ𝑣𝑎𝑝,68.8𝐶 = 28.88 [
]
𝑚𝑜𝑙
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SW
•A rigid vessel contains 50.0 kg of saturated liquid
water and 4.3 kg of saturated vapor. The system
pressure is at 10 kPa. What is the minimum
amount of heat needed to evaporate all the
liquid?
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Thermodynamic Cycles and the Carnot Cycle
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Reversible Processes in Closed Systems
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Open-System Energy Balances on Process
Equipment
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