this presentation will help to understand the basics of thermodynamics in the view chemical engineering aspects.

1. ChemicalEngineeringThermodynamics
Introduction and First law of Thermodynamics
Prepared by
Heena N Katariya
Assistant Professor
S. S Agrawal Institute of Engineering & Technology
S. S. AGRAWAL INSTITUTE OF ENGINEERING & TECHNOLOGY [123]
CHEMICAL ENGINEERING DEPARTMENT

2. Contents
• Subject introduction
• Chapter 1 introduction
• Scope of thermodynamics
• Basic terminology for understanding thermodynamics
• Measurement of amount or size, force, pressure
• Zeroth law of thermodynamics and Temperature
• Making of thermometer
• Ideal gas temperature scale
• Work, energy, heat, heat reservoir
• Heat engine and heat pump
• State and path function
• Internal energy
• Steady state and equilibrium
• Phase rule
• Reversible and irreversible processes
• Joule’s experiments
• General statement of first law of thermodynamics
• First law of thermodynamics for cyclic process
• Internal energy as a state function
• First law of thermodynamics for non-flow process
• Enthalpy
• First law of thermodynamics for flow process
• Heat Capacity

3. Subject introduction
• By studying this subject one can be able to relate the fundamental
of thermodynamics in real life application, can be able to
calculate the thermodynamic properties for any chemical species
or mixtures.
• This particular subject comprises total 7 chapter.
1. INTRODUCTION AND FIRST LAW OF
THERMODYNAMICS
2. VOLUMETRIC PROPERTIES OF PURE FLUIDS
3. HEAT EFFECTS
4. SECOND LAW OF THERMODYNAMICS
5. THERMODYNAMIC PROPERTIES OF FLUIDS
6. THERMODYNAMICS OF FLOW PROCESS
7. REFRIGERATION AND LIQUEFACTION

4. Ch 1 INTRODUCTIONAND FIRST LAW OF
THERMODYNAMICS
• This chapter includes following topics mainly emphasizes on introduction
and basic concept that will make ease in understanding concepts and
fundamentals.
The scope of thermodynamics
Dimensions and units
Measures of amount or size, Force, temperature, pressure, work, energy,
heat, etc.
Internal Energy, Enthalpy
The first law of thermodynamics
Thermodynamic state, state functions
Energy balance for closed systems, Equilibrium,
The Phase rule
The reversible process
Heat capacity
Application of first law of thermodynamics to steady state flow process

5. Scope of Thermodynamics
What is the max work obtained from
the a specified change in system??
What is the min work required to
make specific change in the system??
What is the efficiency with which
work is produced when a certain fuel
is burned.
Answer to all these questions are provided by thermodynamics
• It also helps to determine a priori whether a proposed process
is possible or not.
• It enables one to calculate the equilibrium conditions for
physical and chemical changes.
• It benefits to derive information on the possible side reactions
and method for eliminating undesired side reaction.
• It also help in selecting the optimum reaction condition such as
temperature, pressure, concentration of reactants etc.

6. Scope of Thermodynamics
CAN
• Tell us whether a
chemical reaction is
possible or not.
• Tell us about the driving
force.
• Rate = driving force/
resistance.
CAN’T
• Say whether a possible
reaction will actually
occur or not.
• Unable to give the
information regarding
resistance to flow of
energy or material.
• Tell the at what rate the
system approaches
equilibrium.

7. Basic terminology for understanding
thermodynamics
• System: In thermodynamics, a substance or group of substance in which
we have special interest is called system.
• Process: The changes taking place within the system is referred to as a
process.
• Surroundings: The part of the universe outside the system and separated
from the system by boundaries is called surroundings.

8. Basic terminology for
understanding thermodynamics
• Homogenous systems: this system is called as a
phase. The system in which the properties are
same throughout or properties vary smoothly
without showing any surface of discontinuity is
said to be a Homogenous system. Ex. Liquid
water in a beaker, column of dust free air above
the earth‟s surface.
• Heterogeneous system: this system consists of
two or more distinct homogenous region or
phase. Ex. A liquid mixture of benzene and water.

9. Basic terminology for
understanding thermodynamics
• Closed system: systems that can exchange energy with the
surroundings but which cannot transfer matter across the
boundaries are known as closed system.
• Open system: systems that can exchange both mass and
energy with the surroundings are known as open system.
• Isolated system: systems that that cannot exchange the mass
and energy with surroundings are known as isolated system.

10. Basic terminology for
understanding thermodynamics
• State: Certain specifications such as a pressure, volume and
temperature are necessary to define the conditions of a given
system. The condition defined by such specifications is called
the state of the system
• Properties: the variables used to define the state are called
state functions or properties of system.
• Extensive properties: properties depend upon the quantity of
matter specified in the system are known to be Extensive
properties. Ex. Mass and volume.
• Intensive properties: properties that independent of the size of
the system are known to be intensive properties. Ex. Pressure,
temperature, specific volume, density, etc.

11. Basic terminology for understanding
thermodynamics
Intensive
• Independent property
• Size does not change
• It cannot be computed
• Can be easily identified
• Example: Temperature,
pressure, density,
Specific heat etc.
Extensive
• Dependent property
• Size changes
• It can be computed
• Cannot be easily
identified
• Example: length, mass,
weight, volume, heat
capacity,
Difference between intensive and extensive property

12. Measurement of amount or
size
• Three measures of amount or size are in common
use:
1. Mass, m
2. Number of moles, n
3. Total volume, 𝑉 𝑡
• Number of moles = weight of
substance/molecular weight of substance
• Specific volume= volume/mass = , 𝑉 𝑡
/m
• Molar volume=volume/no of moles= , 𝑉 𝑡
/n

13. Force
• According to Newton‟s law of motion, the force acting on a
body is directly proportional to the time rate of change of
momentum.
• F 𝛼 𝑚 𝑎
• F= cma, where F is the force, m is the mass of the body and a
is the acceleration and c is the proportionality constant. There
are two ways of selecting the constant (c)
• One is setting it as a unity
• Another is choice of constant c yields the technical unit of
force and is defined as a fundamental quantity.
• Thus the constant c becomes dimensionless quantity,
• c=1/ 𝑔 𝑐
• Now F= (1/ 𝑔 𝑐) ma

14. Choice of selection for value of “c”
1. C=1 . When the force is expressed in unit newton.
• 1 Newton (SI unit) : it is the force which is applied to 1 kg mass of
substance produces acceleration of 1 m/s2.
2. C=1/ 𝑔𝑐 , when the force is expressed in kgf (kilogram force)
• 1 kgf (MKS unit): it is the force which accelerates 1 kilogram mass
9.80665 m/s².
• In this case newton‟s second law must include a dimensional
proportionality constant.
• F= (1/ 𝑔𝑐) ma
• Whence 1kgf= (1/ 𝑔𝑐) *1kg* 9.80665 m/s²
• And 𝑔𝑐= 9.80665 kg m/kgf s²
• (kg and kgf both are different unit and do not cancel one another).
• When an equation contains both kg and kgf, the dimensional less
constant 𝑔𝑐 must appear in the equation to make it dimensionally
correct.

15. Difference between 𝒈 and 𝒈 𝒄
𝒈
• 𝒈 stands for Acceleration
due to gravity.
• The acceleration
experienced by a body
under free fall due to the
gravitational force of the
massive body.
• Changes from place to
place.
• Acceleration due to gravity
of earth is 9.8m/s2
𝒈 𝒄
• 𝒈 𝒄 stands for universal
gravitational constant or
newton‟s law conversion
factor.
• The force of attraction
between two objects with
unit mass separated by unit
distance at any part of this
universe.
• Constant at any point in
this universe.
• 𝑔 𝑐= 9.80665 kg m/kgf s²

16. Pressure
• pressure (P) exerted by a fluid on a surface is defined as the normal
force exerted by fluid per unit area of the surface.
• P=F/A
• The unit of pressure in the SI system is newton per square meter
(N/m2), also called as pascal (Pa).
• 1 bar= 10^5 pa= 10^5 N/m²
• The pressure exerted by the atmosphere is called the atmospheric
pressure and it varies with location and elevation on the earth‟s
surface.
• One standard atmospheric pressure abbreviated as the atm.
• atm pressure is the pressure exerted by the earth‟s atmosphere at sea
level.
• 1 atm pressure=1.01325 * 10^5 N/m²
=1.01325*10^5 Pa=101.325 kPa

17. Pressure (Introduction to height of
mercury column)
• Pressure is sometimes expressed in terms of the height of the
column of mercury at 273 K in a standard gravitational field.
• Vertical column of a given fluid under the influence of gravity
exerts a pressure at base in direct proportion to its height and
height of fluid column is equivalent to pressure.
• For the vertical column containing fluid the mass of fluid is
given by,
• m = volume * density m = Ahρ Where A= cross sectional area
of the column, h= its height, ρ = fluid density.
• P= F/A = mg/A = Ahρg/A = hρg
• For vertical column containing mercury at temp of 273 K in a
gravitational filed, at standard atm pressure (101.325 kPa)
height of mercury is 0.76 m (760mm or 760 torr).
• 101.325 kPa= 760 mm Hg.=1 atm

18. Zeroth law of thermodynamics and
Temperature
• Zeroth law of thermodynamics states that : If body A is in thermal
equilibrium with B and B is in thermal equilibrium with C, then C is also in
thermal equilibrium with A.
• Temperature: it measures the degree of hotness or coldness of a body.
• Hotness or coldness does not give a quantitative measure of temperature.
• There is need to device some methods for defining and measuring
temperature.
• The zeroth law allows us to build thermometer which are devices that
indicate the change in temperature by the changes in some physical
properties of the thermometer fluid.
• Such properties are called the thermometric properties.
• Commonly used thermometric properties are:
1. Volume of gases and liquids (thermometers)
2. Pressure of gases at constant volume (constant volume gas thermometer)
3. Electrical resistance of solids (thermistors)
4. Electromotive forces of two dissimilar metals (thermocouples)
5. Intensity of radiation (pyrometrs)

19. Making of thermometer
• Consider a glass capillary filled with mercury, to assign numerical values to
the temperature, there should be some reference states, the temperature of
which are known.
• The reference state chosen are the ice point and normal boiling point of
water.
• In the Celsius scale of temperature , these two reference states are arbitrarily
assigned values 0° C and 100° C, respectively.
• The interval between these two reference points is divided into 100 equal
parts and each part is designated as one degree Celsius.
• In this method , relative expansion of glass, mercury with the temperature
used as thermometric property. And it should be linear with temperature
otherwise different temp scale will indicate the same readings only at the
fixed point.
• Units of temperature are :kelvin (K) , Celsius (°C) most commonly used
• kelvin is the SI unit of temperature
• Another two units used by engineers in US: Rankine and fahrenheit scale.
• Conversion to be remember :
• t (°C)= T(K) -273.15
• t (°F)= 1.8 t(°C) +32
• T(R)= 1.8 T (K)

20. Ideal gas temperature scale
Background:
• Thermometric property for temperature measurement should be
linear with temperature otherwise different temp scale will indicate
the same readings only at the fixed point.
• To overcome this difficulty, a temperature scale does not depend on
the nature of the thermometric fluid is desired.
• Solution to this problem is use of “Ideal gas temperature scale” as an
absolute temperature scale
Basis:
• From the kinetic theory, for ideal gas product of pressure and volume
varies linearly with temperature.
• The ideal gas equation PV=RT, where R is a ideal gas constant and V
is the molar volume of the gas.
• All real gases behaves ideally as pressure reduces to zero.
• Thus, regardless of the nature of gas, the PV product approaches
same value at given temperature for all gases, as P→ 0.
• Thus the quantity PV can be used as a thermometric property to
measure temperature.

21. Ideal gas temperature scale
• suppose a low pressure gas is confined in a constant volume gas thermometer as shown in
figure.
• It is brought into contact with system whose temperature is to be measured.
• By raising or lowering the tube containing mercury, the volume of the gas in the bulb can be
maintained at the level M indicated in the figure.
• The height h of the mercury column indicates the pressure P
of the gas.
• If the thermometer is now brought into contact with a
system at the reference state, and the pressure P∗
, then
𝑇
𝑇∗ =
𝑃𝑉
(𝑃𝑉)∗
Since the volume is maintained constant, 𝑉 = 𝑉∗
.
𝑇
𝑇∗
=
𝑃
𝑃∗
• The reference temperature chosen is the triple point of
water (𝑇∗
= 273.16 K).
• Thus by bringing the thermometer in contact with the
system and by measuring the pressure P of the gas, the T is
given by
𝑇 = 𝑇∗ 𝑃
𝑃∗= 273.16
𝑃
𝑃∗
• Where P∗
is the pressure indicated by the thermometer in
equilibrium with the triple state of water.

22. work
• Work is performed whenever a force acts through a distance.
dW=F dZ----------(1)
• Where W= work done, F=force acting and Z= the displacement.
• The unit of work in SI system is N m (newton meter) or J (joule).
• Understanding work in terms of gas expansion or compression:
• Assume the gas confined in a cylinder .
• P= pressure of gas and V= volume of gas in cylinder.
• A= surface area of the piston exposed to the gas.
Force F =PA ----------(2)
• The displacement of the piston in the direction of the force dZ is
related to change in volume dV of the gas as
𝑑𝑍 =
𝑑𝑉
𝐴
------------(3)
• From equation (1), (2), and (3),
dW= P dV------------(4)

23. work
• If the volume of the gas changes from the initial value 𝑉1 to the
final value 𝑉2, then equation dW= P dV may be integrated to
get work done on the face of the piston.
• 𝑤 = 𝑝 𝑑𝑉
𝑉2
𝑉1
---------------(5)
• The integral of equation (5)
is given by the area under
the curve between the limits
𝑉1 and 𝑉2.
• The area, and hence the
work done in the
compression or expansion
of the gas depend on the
shape of the PV curve.

24. Energy
• Kinetic energy: when F force is applied to body having m kg of mass, then it
will be displaced a distance dl during differential interval of time dt.
• Therefore dw=F dZ= ma dl-------------(1) (unit : joule (SI), kgf m (MKS))
• Here m= mass of body,
a= acceleration of body= du/dt
u= velocity of the body
• Now, dW=m
𝑑𝑢
𝑑𝑡
dl= m
𝑑𝑙
𝑑𝑡
du------------(2)
• Velocity u=
𝑑𝑙
𝑑𝑡
, therefore equation (2) becomes,
• dW= m u du -----------(3)
• For the change in velocity from 𝑢1 to 𝑢2, energy will be
• W= m 𝑢 𝑑𝑢
𝑢2
𝑢1
=m(
𝑢2
2
2
−
𝑢1
2
2
)= ∆(
𝑚𝑢2
2
)------------(3)
• This equation (3) shows the work done on a body in accelerating it from intial
velocity 𝑢1 to final velocity 𝑢2.
• Each of the quantity
1
2
m𝑢2 of equation (3) is a kinetic energy, introduced by
Lord Kelvin.
• 𝐸 𝑘=
1
2
m𝑢2
----------(4)

25. Energy
• Potential energy: Energy possessed by the system due to its
position above some arbitrary reference plane is referred to as
its potential energy.
• If mass m is at an elevation z above the ground, the work done
is,
• dW=F dZ=mg dZ--------------(1)
• Let the body is raised from initial level 𝑍1 to the level 𝑍2,
• W= mg 𝑑𝑍
𝑍2
𝑍1
= mg(𝑍1-𝑍2)----------(2)
• Each of the quantity in equation (2) mgZ is known as potential
energy.
• 𝐸 𝑝=mgZ--------(3)

26. Heat
• When a hot object brought into contact with a cold object , hot object
becomes cooler and cold object becomes warmer.
• That means there is something transferred from hot object to cold object.
And we call it as a Heat.
• Heat: it is the quantity which is transferred between bodies due to
temperature difference existing between them.
• Heat always flows from higher temperature to lower temperature.
• In thermodynamic sense, heat is never regarded as being stored within
the body.
• Like work, it exists only as energy in transit from one body to another or
between system and surroundings.
• When energy in the form of heat is added to body, it is stored not as a
heat but as a kinetic energy and potential energy of the atoms and
molecules of the body.
• Units of heat are joules (J), calorie (cal) and British thermal unit (BTU).
• 1 calorie=4.1868 J
• 1 BTU= 1055.04 J

27. Heat reservoir
• Heat/ thermal reservoir: A thermal reservoir is
a sufficiently large system in stable equilibrium
from which finite amount of heat can be
transferred without any change in its temperature.
• Heat source / High temperature reservoir
(HTR): a heat source is a high temperature
reservoir (HTR) from which heat is transferred.
• Heat sink / Low temperature reservoir (LTR) :
a heat sink is a low temperature reservoir (LTR)
to which heat is transferred.

28. Heat engine and Heat pump
Heat Engine
• It is a thermodynamic system
operating in a cycle to which heat
is transferred and from which
work is extracted
• The thermal efficiency of a heat
engine (𝜂) is defined as the ratio
of work output to the heat input.
Heat Pump
• It is a thermodynamic system operating
in a cycle that removes heat from a low
temperature body and delivers it to a
high temperature body. (external energy
in the form of work is necessary to
accomplish this).
• The coefficient of performance of a heat
pump (COP) is defined as the ratio of
heat transferred from low temperature
reservoir to work output.
E
HTR
LTR
W
𝑄1
𝑄2
P
HTR
LTR
𝑄1
𝑄2
W COP=
𝑄2
𝑊
𝜂 =
𝑊
𝑄1

29. State and Path function
State function
 properties of substance defines it‟s
present system and do not give a
record of its previous history is
known as state function.
 Do not depend upon the path by
which the state was arrived.
 Explanation: let M=property of the
system
• ΔM= change in the property M as it
changes from state 1 to state
• Value of ΔM is the same for
whatever path is used to changes
from state 1 to state 2.
 For a cyclic process ΔM is zero as
the initial and final state are same.
 Internal energy is a state function,
Path function
 Properties of substance that not
only determined by the initial and
final state but it also depend upon
the at which manner changes are
being carried out. (i.e., properties
that depend upon the path to make
change in the system.)
 Explanation: heat and work
associated a given change in state
vary with path from initial to final
state,
 Heat and work are path function.

30. Internal energy
• The energy stored in the system by virtue of the arrangement and
motion of the molecules constituting the system is called internal
energy. It is denoted by “U”.
• The molecules of the system possess kinetic energy of rotation,
translation and vibration. And also possess potential energy due to
force of attraction existing between them.
• These molecular potential and kinetic energy contribute to an internal
energy of the system.
• The energy due to mass motion of the system as a whole ( kinetic
energy) and that due to external position in a gravitational force or
magnetic field (the potential energy) are not included in internal
energy.
• In a cyclic process, U (initial state)= U (final state).
• During the non cyclic process, some energy gets stored in the system
or some stored energy gets removed from the system. 2
• These changes in the stored energy are measured as the change in
internal energy of the system.

31. Steady state and equilibrium
• Steady state: a system, which is interacting with the
surroundings is said to have attained steady state condition
when the properties at a specified location do not vary with
time.
• Example: consider the walls of furnace, the inside surface of
which is exposed to hot combustion gases and the outside
surface to atmospheric air.
• Heat transfer occurs from the inside of the furnace to the
outside and the temperature at a specified location in the wall
varies with time.
• When the temperature at specified location or any point do not
vary with time, the wall is said to attain the steady state
condition.

32. Steady state and equilibrium
• Equilibrium: a system is said to be in a state of equilibrium if
the properties are uniform throughout and do not vary with the
time.
• Consider here properties on macroscopic level.
• A system is in thermal equilibrium when no heat exchange
occurs between various points within the system and the
temperature is uniform throughout.
• For the system in mechanical equilibrium, the pressure is
uniform.
• The state of equilibrium may be treated as the one in which all
forces are in exact balance.
• The state of equilibrium will be retained by the system after
any small, but short mechanical disturbance in the external
conditions.

33. Phase rule
• For any system at equilibrium, the number of independent variables
that must be arbitrarily fixed to establish its intensive state is given by
the celebrated phase rule of J. Willard Gibbs.
• This is represented as follow.
F= C-P+2
• Where F = number of degrees of freedom (The number of
independent variables necessary to define the state of equilibrium
uniquely is known as the number of degrees of freedom.)
• C= the number of chemical species.
• P = number of phases present at equilibrium.
• The intensive state of a system at equilibrium is established when its
temperature, pressure, and the compositions of all phases are fixed.
• The phase-rule variables are intensive properties, which are
independent of the extent of the system and of the individual phases.
• Thus the phase rule gives the same information for a large system as
for a small one and for different relative amounts of the phases
present.

34. Reversible and irreversible process
• Processes occur when there exists a driving force for a change
of state between parts of the system or between the systems
and surroundings.
• If this driving force is finite, the process is irreversible and if it
is infinitesimal in magnitude, the process reversible.
• All spontaneous processes occurring in nature are irreversible.
They can not be reversed without the use of external energy.
• If the system undergoing an irreversible process were to be
brought back to its initial state, surroundings would have to
undergo some change though heat and work interactions.
• Examples: diffusion of a solute from a concentrated solution to
dilute solution, transfer of heat from hot body to cold body,
rusting of iron in the presence of atmospheric oxygen.

35. Irreversible expansion of gas
• Consider a gas at high pressure is confined in a piston-cylinder
arrangement. The piston is held in position by placing a suitable
weight W over it.
• The pressure of the gas= atm pressure and the weight of the piston
including weight placed on it.
• Assume that the piston-cylinder neither absorb nor transmit heat
and piston has frictionless motion in cylinder.
• Suppose W is removed by sliding it into the compartment on the
side.
• Due to the force imbalance, the piston rises up as shown in figure.
• The work done by gas on expansion against atm is not available
for restoring the gas to its initial state.
• If gas returns to its original state, work would be done on the
system and therefore surrounding undergoes some change and
the process is clearly irreversible one.
• As W is removed from the piston, and piston was held to this
higher level, due to expansion of gas, the potential energy of
surroundings would increase and by utilizing the increment in
potential energy , the state of system can be restored.
• But this is not happening because the weight removed from the
piston is at the same level as it was before the expansion of the
gas.
• There for work can not be measured as 𝑤 = 𝑃 𝑑𝑉

36. Work done by expansion of gas
• The work of expansion by the gas against the atmosphere is the product of
force and the displacement.
• Let F= force acting downwards
• dZ= displacement of the piston
• The work done by the gas against atmosphere = 𝑤 = 𝐹 𝑑𝑍
• When the force acting downwards and the gas pressure are in exact balance,
F=PA, Where A= area of the piston.
• Therefore work done by the gas against atmosphere= 𝑤 = 𝑃𝐴 𝑑𝑍 = 𝑃 𝑑𝑉
• Here dV= increase in volume due to expansion.
• Once the weight W is removed from the piston the forces are out of balance,
that is the force exerted by gas and the downward force are not equal.
• In this case it is incorrect, if the work is appearing in the surrounding is
evaluated as 𝑃 𝑑𝑉 .
• it is only for the reversible process where the forces are always in exact
balance and the work done by the system is evaluated from the properties of
system.

37. Reversible expansion of gas
• Expansion of the gas can be reversed if the weight on the piston is replaced by infinitely large
number of fine particles together weighing W.
• If the particles were removed one at a time, the pressure of the gas would never be out of
balance with the downward forces.
• When the entire weight is removed from the piston, the potential energy of the surroundings is
increased, as is evident from the height of the pile obtained on the side.
• The system does maximum useful work on the surroundings.
• The weights can be replaced one by one on the piston and the piston can be made to retrace its
path without using any extra energy from the surroundings.
• This is a reversible process, as the process can be reversed at any instant by an infinitesimally
small increase in downward forces and the original state of the system is restored without any
change in the surroundings.
• Now we can calculate work done by the expansion as 𝑤 = 𝑃 𝑑𝑉.

38. Characteristics of reversible process
• In a reversible process, the driving and opposing forces are in
exact balance, and an infinitesimal change in the external
conditions would cause a reversal in the direction of the
process.
• For reversible process to occur, friction, turbulence, and other
dissipative effects should be absent.
• It takes an infinite time for its completion.
• A reversible process occurring in a work-producing machine
delivers the maximum amount of work and that occurring in a
work-requiring machine requires the minimum amount of
work.
• A reversible process is an idealised and imaginary concept and
may be used for the comparison of the performance of actual
systems and for indicating the efficiency of processes.

39. Joule’s experiments
• Joule's experiments were simple
enough, but he took elaborate
precautions to insure accuracy.
• He placed known amounts of
water, oil, and mercury in an
insulated container and agitated
the fluid with a rotating stirrer.
The amounts of work done on the
fluid by the stirrer were
accurately measured, and the
temperature changes of the fluid
were carefully noted.
• He found for each fluid that a
fixed amount of work was
required per unit mass for every
degree of temperature rise caused
by the stirring, and that the
original temperature of the fluid
could be restored by the transfer
of heat through simple contact
with a cooler object.
• Thus Joule was able to show
conclusively that a quantitative
relationship exists between work
and heat and, therefore, that heat
is a form of energy.
Conclusion: In experiments such as those conducted by Joule,
energy is added to a fluid as work, but is transferred from the fluid
as heat. What happens to this energy between its addition to and
transfer from the fluid? A rational concept is that it is contained in
the fluid in another form, called internal energy.

40. General statement of first law of thermodynamics
• The idea of designing an engine that would produce
mechanical work continuously without drawing energy
from external sources and without undergoing a change
had been a great fascination for scientists and engineers.
• The failure to construct such a perpetual motion machine
(PMM) formed the basis for the law of conservation of
energy
• The fundamental implication of this law is that “although
energy may be converted from one form to another, it
cannot be created or destroyed”.
• Whenever a quantity of one form of energy is produced,
an exactly equivalent amount of another kind must be
used-up.

41. First law of thermodynamics for cyclic process
• Consider a static system undergoing a cycle of changes. Work is done on the
system by forces acting from the surroundings, or vice versa, and heat is
transferred between the system and the surroundings during the process.
• Then, according to the first law of thermodynamics, the algebraic summation of
all work effects exactly equals the summation of all heat effects.
• Let Q = heat added to the system and W=work done by the system. (Q is negative
when heat is rejected by the system and W is negative when work is done on the
system ).
• If work and heat both are measured in consistent units
𝑊 = 𝑄
• If the units chosen for heat and work are different, then above equation can be
written as,
𝑊 = 𝐽 𝑄
• J is the mechanical equivalent of heat if the work is mechanical, and electrical
equivalent of heat if work is electrical.

42. Internal energy as a state function
• A system undergoing changes from state 1 to state 2
along path a.
• Let the initial condition be restored along path b.
• If the surrounding remains unchanged, the change in
internal energy (ΔU) along path a = - the change in
internal energy (ΔU) along path b.
• If (ΔU) along path b < (ΔU) along path a, there would
be residuum of energy resulting from this cyclic
operation.
• That means energy would have been created without
loss of an equivalent amount of another kind. That is
not true. Therefore energy changes along paths a and
b should be numerically same.
• On the same basis (ΔU) along path along path c and
d also should be numerically equal but opposite in
sign to ΔU along path a .
• Here paths b, c, and d are different routes for
changing state of the system from state
• to state 1.
• Therefore the internal energy change only depends
upon the final and initial state, proving that internal
energy is a state function.

43. First law of thermodynamics for non-flow process
• The first law of thermodynamics requires that the total energy change of the system must be
an equal but in opposite sign in the total energy change of the surroundings, so that, there is
no net change in the energy in any process.
• The change in the total energy of the surroundings occurs only through the exchange of heat
or work with the system. Then the change in the total energy of the surroundings,
∆𝐸𝑠𝑢𝑟 must be equal to the energy transferred to or from it as heat and work.
• Since Q is the heat transferred to the system and W is the work extracted from it during the
process,
∆𝐸𝑠𝑢𝑟 =-Q+W ………………………………….(1)
• For a closed system undergoing only changes in the kinetic, potential, and internal energies,
the total energy change of the system ∆𝐸𝑠𝑦𝑠 is given by,
∆𝐸𝑠𝑦𝑠 = ∆𝐾𝐸 + ∆𝑃𝐸+ ∆𝑈 … … … … … … … … … … … … …(2)
• Since ∆𝐸𝑠𝑦𝑠 = - ∆𝐸𝑠𝑢𝑟 from equation (1) and (2),
∆𝐾𝐸 + ∆𝑃𝐸+ ∆𝑈= Q-W -----------------------------(3)
• For a steady-state non-flow process ∆𝐾𝐸 = 0 and ∆𝑃𝐸=0,
∆𝑈= Q-W------------------------------------(4)
• For differential changes in the thermodynamic state of closed system, eq (4) becomes
dU= dQ-dW ----------------------------------(5)
• Equation (4) and (5) are the mathematical statements of the first law of thermodynamics for
non-flow process.

44. Enthalpy
• For system kept at constant volume, there is no work done in the system and ∆𝑈=Q (heat
supplied to system).
• When system is free to change its volume against a constant external pressure, ∆𝑈≠ Q.
• In fact a part of energy supplied is utilized by system to occupy a new volume, the energy
than utilized is equal to work required to push the surrounding against constant pressure.
• Consequently ∆𝑈< Q .
• However the heat supplied at constant pressure can be measured as the change in another
thermodynamic property of the system, which we call enthalpy. It is defined as,
H=U+PV
• Here U= internal energy of the system,
• P= absolute pressure,
• V= volume of the system.
• U,P,V are all state functions, therefore Enthalpy H is a state function.
• The product, PV, represents the work that must have been done against an environmental
pressure P to create a volume V occupied by the system, or rather, the energy that the
system possesses because of it occupying a space.
• Thus, enthalpy may be treated as „total energy‟, because it includes both the intrinsic
energy it possesses (U) and the energy due to the expansion possibilities of the system
(PV).

45. Enthalpy
• As per definition of enthalpy,
H =U+ PV------------------(1)
• In differential form equation (1) can be written as,
dH= dU+ d(PV)----------------(2)
• Since all the term in equation (2) are state functions,
ΔH= ΔU+ Δ(PV) -----------------(3)
• Equation (3) is applicable for any finite change ocuuring in the system,
1. ΔH for mechanically reversible, non flow process at constant pressure,
dH = dU+PdV+VdP------------------(4)
dH = dQ-dW+pdV+VdP-------------(5)
• dW= P dV for a reversible non flow process and V dP = 0 for constant
pressure process, equation (5) becomes
dH=dQ (constant pressure process)-------------------------(6)
2. ΔH for process occurring at constant volume,
dU= dQ (constant volume process) -------------------------(7)

46. First law of thermodynamics for flow process
Figure Description :
• Consider an idealised flow system as shown in Fig. 2.4. A fluid is flowing
through the apparatus from section 1 to section 2.
• The velocity, specific volume, pressure, and height above the datum are
represented by u, V, P, and Z respectively.
• The suffix 1 indicates conditions at section 1 and suffix 2 the conditions at
section 2.
• Heat Q is added per unit mass of the fluid by means of the heat exchanger
and shaft work 𝑊𝑠 is extracted by means of a turbine or any other suitable
device.

47. First law of thermodynamics for flow process
Derivation:
• According to the first law of thermodynamics, the total energy with which the fluid is entering at section 1 plus the energy
imparted to the fluid while it is in the system must be equal to the total energy with which the fluid is leaving the system at
section 2.
• The contributions to the total energy at section 1 are: internal energy + potential energy + kinetic energy + entrance work
• Total energy at section 1=𝑚𝑈1 + 𝑚𝑔𝑍1 +
1
2
𝑚𝑢1
2
+ 𝑚𝑃1 𝑉1
• The energy at section 2 is also made up of similar quantities. The force at section 1 does work on the system, while at
section 2, work done by the system on the surroundings.
• Total energy at section 2=𝑚𝑈2 + 𝑚𝑔𝑍2 +
1
2
𝑚𝑢2
2
+ 𝑚𝑃2 𝑉2
• The energy imparted to the fluid within the system is determined by knowing the amount of heat exchanged between the
system and surroundings and the total work done by the system or work done on the system.
• Total energy imparted to the fluid =𝑚𝑄 − 𝑚𝑊𝑠
• combining the preceding three results,
𝑚𝑈1 + 𝑚𝑔𝑍1 +
1
2
𝑚𝑢1
2
+ 𝑚𝑃1 𝑉1+ 𝑚𝑄 − 𝑚𝑊𝑠=𝑚𝑈2 + 𝑚𝑔𝑍2 +
1
2
𝑚𝑢2
2
+ 𝑚𝑃2 𝑉2
𝑈1 + 𝑔𝑍1 +
1
2
𝑢1
2
+ 𝑃1 𝑉1+ Q−𝑊𝑠=𝑈2 + 𝑔𝑍2 +
1
2
𝑢2
2
+ 𝑃2 𝑉2
Q−𝑊𝑠=𝑈2 − 𝑈1 + 𝑔𝑍2 − 𝑔𝑍1 +
1
2
𝑢2
2
−
1
2
𝑢1
2
+ 𝑃2 𝑉2 − 𝑃1 𝑉1
Q−𝑊𝑠=∆𝑈 + 𝑔∆𝑍 +
1
2
∆𝑢2
+ ∆ 𝑃𝑉
∆𝑈 + ∆ 𝑃𝑉 + 𝑔∆𝑍 +
1
2
∆𝑢2
= 𝑄 − 𝑊𝑠----------------------------------------------(1)
∆𝐻 + 𝑔∆𝑍 +
1
2
∆𝑢2
= 𝑄 − 𝑊𝑠----------------------------------------------------------(2)
• Equation (2) is the mathematical statement of first law of thermodynamics for flow processes and can be used for solving
problems involving flow of fluids, power required for pumps and compressors, etc.
• For most applications in thermodynamics, the kinetic energy and potential energy terms in equation (2) are negligibly small
compared to the other. So that
∆𝐻 = 𝑄 − 𝑊𝑠---------------------------------------------------------------------------(3)

48. Heat capacity
Heat capacity: The heat capacity of a substance is the quantity of heat to
be supplied to effect a temperature rise of one degree.
𝑑𝑄 = 𝐶 𝑑𝑇
• Where C is known as heat capacity of the substance.
• Heat capacity of unit mass of a substance is also known as specific heat
of substance,
• The heat capacity depends on the way in which heat is supplied.
Heat capacity at constant volume:
• when heat is supplied to a system at constant volume , work done is zero
and the quantity of heat required is given by,
𝑑𝑄 = 𝐶 𝑉 𝑑𝑇 (𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑣𝑜𝑙𝑢𝑚𝑒)-----------------(1)
• Where 𝐶𝑣 = heat capacity at constant volume.
𝐶 𝑉 = (
𝜕𝑄
𝜕𝑇
) 𝑉------------------(2)
• As per first law of thermodynamics, 𝑑𝑈 = 𝑑𝑄 − 𝑑𝑊.
• For constant volume process, 𝑑𝑊 = 0 𝑡𝑕𝑒𝑟𝑒𝑓𝑜𝑟𝑒 𝑑𝑈 = 𝑑𝑄 and
equation (2) becomes,
𝐶 𝑉 = (
𝜕𝑈
𝜕𝑇
) 𝑣------------------(3)
𝑑𝑈 = 𝐶 𝑉 𝑑𝑇------------------(4)

49. Heat capacity
Heat capacity at constant pressure:
• If heat is supplied to a substance at constant pressure, it is free to expand doing work against the constant
pressure.
• A part of the heat supplied to the system is utilized for the work of expansion and more heat will be required
to raise the temperature than that required in a constant volume process for the same temperature change.
𝑑𝑄 = 𝐶 𝑃 𝑑𝑇 (𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒)-------------------(1)
• Where 𝐶 𝑃= heat capacity at constant pressure.
𝐶 𝑃 = (
𝜕𝑄
𝜕𝑇
) 𝑃------------------(2)
• As per first law of thermodynamics, 𝑑𝑈 = 𝑑𝑄 − 𝑑𝑊 −−−−−−−−−− −(3)
• Here 𝑑𝑊 = 𝑃 𝑑𝑉, therefore 𝑑𝑈 = 𝑑𝑄 − 𝑃 𝑑𝑉 −−−−−−−−−−−−− −(4)
• We know that 𝐻 = 𝑈 + 𝑃𝑉---------------------------------(5)
𝑑𝐻 = 𝑑𝑈 + 𝑃 𝑑𝑉 + 𝑉 𝑑𝑃-----------------(6)
𝑑𝑈 = 𝑑𝐻 − 𝑃 𝑑𝑉 − 𝑉 𝑑𝑃-----------------(7)
• Putting the value of dU in equation (4),
𝑑𝐻 − 𝑃 𝑑𝑉 − 𝑉 𝑑𝑃 = 𝑑𝑄 − 𝑃 𝑑𝑉------------------(8)
𝑑𝐻 − 𝑉 𝑑𝑃 = 𝑑𝑄----------------(9)
𝑑𝐻 = 𝑉 𝑑𝑃 + 𝑑𝑄----------------(10)
• For constant pressure process dP=0, equation becomes,
𝑑𝐻 = 𝑑𝑄----------------(11)
• Now equation (2) can be written as,
𝐶 𝑃 = (
𝜕𝐻
𝜕𝑇
) 𝑃------------------(12)
𝑑𝐻 = 𝐶 𝑃 𝑑𝑇-----------------(13)

50. References:
• “Introduction to Chemical Engineering Thermodynamics”; J.
M. Smith, H. C. Vanness, M. M. Abbott, The McGraw-Hill
Companies, Inc.
• “A text book of Chemical Engineering Thermodynamics”; K.
V. Narayanan, Prentice-Hall of India Pvt. Ltd.