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Thermodynamics
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Chapter Overview
1. Heat and Thermal energies transferred form a region of higher temperature
to a region of lower temperature.

2. Internal energy and temperature dependence on it.

3. Gas laws (Boyles, Charles’s laws and general gas equation).

4. Concept of state and path function with example.

5. Thermodynamics and work in thermodynamics.

6. Application of 1st law with relevant equation and graphs.

7. Heat capacity, specific heat capacity and molar heat capacity.

8. CP − CV = Rand value of CP and CV .

​ ​ ​ ​

9. Heat engine with expression for efficiency of heat engine.

10. Entropy and its relation with flow of heat.

11. Some Practice MCQs.

Concepts
Heat
Heat: The energy in transit from hot body to cold body.
S.I Unit: Joule (J)
Other units:

1. In CGS system, unit of heat is ERG.

Thermodynamics 1
 2. FPS unit of heat is B.T.U (British thermal unit).
1 B.T .U = 1055.06 J 
3. According to caloric theory unit of heat is Calorie.
1 Calorie = 4.2 J 
Source: A body or thermal reservoir which radiates heat is called heat
source.
Sink: A thermal reservoir which absorbs heat from a source is called heat
sink.
Modes Of Heat Transfer:

1. Conduction: is heat transfer directly between neighboring atoms or

molecules. Usually, it is heat transfer through a solid.
For Example: When metal spoon is heated from one end, the heat
transfers to other end of spoon due to conduction via vibrating atoms in
spoon.

2. Convection: is heat transfer via the movement of a fluid, such as air or

water.
For Example: Movement of air around campfire OR the motion of water
in pot when started to heat on stove.

3. Radiation: is the emission of electromagnetic radiation. While it occurs

through a medium, it does not require one.
For Example: Sun light carries warmth due to ultraviolet and other
radiations.

Internal Energy

Internal Energy : The total energy stored in a body is termed as its ‘ internal
energy’.

It is the energy form inherent in every system is the internal energy,

which arises from the molecular state of motion of matter.

The symbol ‘U’ is used for the internal energy.

The S.I unit is joules (J).

Thermodynamics 2
 Internal energy is the sum of system’s potential energy and kinetic
energy.

Molecules of hot tea moves more rapidly results in higher K.E, hence
consequently the tea carries higher internal energy.

Temperature

Temperature : The degree of hotness or coldness of body is called its

“Temperature”.

Temperature of body Is linked to its internal energy.

Scales Of temperature:

1. Centigrade Or Celsius Scale:

100 Division (0o C − 100o C).
2. Fahrenheit Scale:

180 Division (32o F − 212o F ).

3. Kelvin Scale:

100 Division (273K − 373K).

0 K  or −273.15o C is lowest possible temperature and called
“Absolute Zero”.

Kelvin scale is also called “Absolute Scale”, Since absolute zero is

actually zero on kelvin scale (lowest possible temperature).

Rankine Scale:
Rankine scale is also absolute scale of thermodynamic temperature as it is
also based on absolute zero.

Thermodynamics 3
 o
R = o F + 459.67  ​

0 o R = 0.0000K
1 o R = 0.55556K
Gas Laws
BOYLE’S LAW:

STATEMENT:

“At constant temperature, the volume of the given mass of the gas is
inversely proportional to the applied pressure.”

MATHEMATICAL EXPRESSION:

If V is the volume and P is the pressure of the given mass of gas, then
according to Boyle’s Law:

P V = Constant  ​

OR

P1 V1 = P2 V2 
​ ​ ​ ​ ​

The above equation is known as two state Boyle’s Isothermal equation of

state of a gas.

CHARLES’S LAW:

STATEMENT:

Thermodynamics 4
 “At constant pressure, the volume of the given mass of the gas is
directly proportional to its absolute temperature.”

MATHEMATICAL EXPRESSION:
If V be the volume of a given mass of the gas and T be the absolute
temperature of the given sample of gas, then according to Charles’s law
at constant pressure:

V
= Constant 
​ ​

T
OR

V1 V2
= 
​ ​

​ ​ ​

T1 T2 ​ ​

This is the two states Charles isobaric equation of the state of a gas.

From the graph of Charles’s law it is found that at 0o C the gas still
possesses a volume Vo . When the straight line of the graph is
​

extended towards negative temperature it intersects the

temperature axis at a value of −273o C . This shows that if a gas
could be cooled to −273o C , it would have no volume ideally. Hence
−273o C is called the ‘Absolute Zero’ of the temperature.

General Gas Law:

P V = nRT ………. (i) ​

Here, Rrepresent ‘General gas constant’ and its value is

8.314 J mol −1 K −1 .

Thermodynamics 5
 Since,
R = kNA  ​

Put the value in equation (i), we get:

P V = n(kNA )T  ​

P V = nNA kT ………. (ii) ​

Since,
Number of molecules of given gas N
NA = ​

Total no of moles ​ = n
​

OR
Number of molecules(N) = nNA  ​

Put value of N in equation (ii), we get:

P V = NkT …………. (iii) ​

Here, K represent ‘Boltzmann constant’ and its value is

1.38×10−23 J /K .
Re-arranging equation (iii), we get:
P= N
V
kT 
OR

P = NV kT  ​ ​

Here, NV shows number of molecules per unit volume of given gas.

​

State And Path Function

State Function: A property whose value doesn’t depend on the path taken
to reach that specific value is known as a state function or point function.

Example: Temperature, Pressure, volume, internal energy, Entropy, etc.

are all state functions.

Path Function: A path function is a property that depends on the path

taken to reach a particular state.

Example: Work, Heat and other energy transfer forms.

Extensive Quantities:

Thermodynamics 6
 Extensive quantities are those that depend upon the amount of material.
Examples would include the volume, density or the heat capacity of a body.

Intensive Quantities:
Intensive quantities do not depend on the amount of material. Temperature
and pressure are examples. Another would be the specific heat capacity of
a substance.

System And Its types

SYSTEM: Anything in the universe which is under consideration or

observation is called ‘system’.
SURROUNDING: Surrounding is immediate effective vicinity of system
which is not under consideration.
BOUNDARY: A real or imaginary, tangible or non-tangible line that
separates a system from its surroundings is known as boundary.
TYPES OF SYSTEM:
There are three types of system:

1. OPEN SYSTEM: Such a system in which transfer of both matter and

energy are possible across the boundary is known as an open system.

E.g. Room, human-being body etc.

2. CLOSED SYSTEM: Such a system in which transfer of matter is not

possible but energy can transfer across the boundary is known as open
system.

E.g. Tube light, bullet etc.

3. ISOLATED SYSTEM: Such a system in which transfer of both matter

and energy is impossible across the boundary is known as isolated
system.
E.g. Thermos flask

Thermodynamics
Thermodynamics:

“The branch of Physics deals with the interconversion of heat energy into
other forms of energy (Mechanical energy, work, etc.) or vice versa is

Thermodynamics 7
 called ’Thermodynamics’. ”

Work In thermodynamics:
In thermodynamics, work performed by a system is the energy transferred
by the system to its surroundings.

A system contains no work, work is a process done by or on a system.

W = F .d
Since,

P = F /A → F = P A
Hence,

W = (P A).∆Y 

W = P (A.∆Y )

W = P ∆V  ​

Zeroth Law OF Thermodynamics:

If two systems are both in thermal equilibrium with a third system, then the
first two systems are also in thermal equilibrium with each other.
OR

Systems that are in thermal equilibrium exist at the same temperature.

Thermodynamics 8
 1st Law Of Thermodynamics
“ Heat energy can convert into work and vice versa but total energy
remains constant “.
OR
”The change in internal energy in any process is equal to net heat flow
from the system minus the total work done” .
MATHEMATICAL EXPRESSION:

∆U = ∆Q − ∆W 
∆U + ∆W = ∆Q
OR

∆Q = ∆U + ∆W  ​

This is the equation of the first law of thermodynamics.

SIGN CONVENTION:

When heat is supplied to the system ∆Qis taken to be positive.

When heat is taken out of the system ∆Qis taken to be negative.

When work is done on the system ∆W is taken to be negative.

When work is done by the system ∆W is taken to be positive.

When there is an increase in the internal energy of the system ∆U is

taken to be positive.

When there is a decrease in internal energy of the system ∆U is taken

to be negative.

Application Of 1st Law Of Thermodynamics:

1. ISOBARIC PROCESS:
“A thermodynamic process in which pressure of the system remain
constant is called isobaric process.”
∆Q = ∆W + ∆U 
∆Q = P ∆V + ∆U 

Thermodynamics 9
 ∆Q = P (Vf –Vi ) + ∆U 
​ ​ ​

This result shows that in an isobaric process, the heat energy supplied
to the system is converted into work done at constant pressure and to
the change in internal energy of the system.

On PV-diagram, isobaric process can be represented by a

horizontal straight line which is also called as ‘isobar’.

2. ISOCHORIC PROCESS:
“The process in which the volume of a system remains constant is
known as an isochoric process.”
P ΔV = ΔW = 0
∆Q = 0 + ∆U 
∆Q = ∆U  ​

The equation shows that the heat energy supplied to system in

isochoric process utilized completely to increase the internal energy of
system.

On PV-diagram, isochoric process can be represented by a vertical

straight line which is also called as ‘isochor’.

Thermodynamics 10
 3. ISOTHERMAL PROCESS:
“The process in which the temperature of the system remains
constant in known as isothermal process.”

∆U = 0
∆Q = ∆W + 0
∆Q = ∆W  ​

This result shows that in an isothermal process, the heat energy

supplied to the system is totally converted into work done. Isobaric
process is a slow process.

On PV-diagram, isothermal process can be represented by a

curve which is called ‘isotherm’.

Thermodynamics 11
 4. ADIABATIC PROCES:

“The thermodynamic process in which no heat energy is

transferred across the boundaries of system is called adiabatic
process”.

∆Q = 0
0 = ∆W + ∆U 
−∆U = ∆W 
∆W = −∆U  ​

This result shows that in an adiabatic process, the work is done at

the cost of internal energy of the system.

On PV-diagram, adiabatic process can be represented by a

curve which is called adiabatic curve or ‘adiabat’.

Heat Capacity
HEAT CAPACITY:
“The amount of heat supplied to the substance to raise its temperature
through 1 kelvin or 1 o C is known as its heat capacity.”

MATHEMATICALLY:

Thermodynamics 12
 ΔQ
c= 
ΔT
​ ​

Where,

ΔQis the amount of heat supplied.

ΔT is the change in temperature.
S.I UNIT:
It is a scalar quantity and its S.I unit is J /K . It can also be measured in
J /C .
SPECIFIC HEAT CAPACITY:
“The amount of heat supplied to raise the temperature of a 1 kg sample of a
substance through 1 kelvin or 1o C is known as its specific heat capacity.”

It is the property of a substance and it depends upon the nature of a

substance but is independent of mass of substance.

MATHEMATICALLY:

ΔQ
C=  ​ ​

mΔT
S.I UNIT:
J
It is a scalar quantity and its S.I unit is K g.K
​ . It can also be measured in
J
K g.o C
.
​

MOLAR SPECIFIC HEAT CAPACITY:

“The amount of heat supplied to raise the temperature of 1 mole of a

sample of a substance through 1 kelvin or 1o C is known as its molar
specific heat capacity.”
• It depends upon nature of substance but is independent of no. of moles.
MATHEMATICALLY:

ΔQ
C′ =  ​ ​

nΔT
S.I UNIT:

Thermodynamics 13
 J
It is a scalar quantity and its S.I unit is mol.K . It can also be measured in​

J
mol.o C .
​

MOLAR SPECIFIC HEAT AT CONSTANT PRESSURE :

“It is the amount of heat required to raise the temperature of one mole of
gas through 1K at constant pressure”.

It is denoted by Cp  ​

Mathematically expression:

ΔQP
CP = 
​

​ ​ ​

nΔT
MOLAR SPECIFIC HEAT AT CONSTANT VOLUME:
“It is the amount of heat required to raise the temperature of one mole of
gas through 1K at constant volume”.

It is denoted by CV  ​

Mathematically expression:

ΔQV
CV = 
​

​ ​ ​

nΔT
Relation Between CP And CV  ​ ​

CP − CV = R 
​ ​ ​

The difference between the molar specific heat at constant pressure and
molar specific heat at constant volume is equal to universal gas constant.

VALUES OF CP and CV : ​ ​

For mono-atomic gas:

According to kinetic theory, for mono atomic gas the value of CV is: ​

3
CV = R
2
​ ​ ​

We know that,
CP − CV = R
​ ​

Thermodynamics 14
 Put value of CV : ​

CP = R + 32 R
​ ​

5
CP = R
2
​ ​ ​

For di-atomic gas:

7
CP = R
2
​ ​ ​

5
CV = R
2
​ ​ ​

Heat Engine
“Convert heat engine into work done is called ‘Heat Engine’ “.

The work done or the useful energy supplied by heat engine is given as:

ΔW = Q1 –Q2  ​ ​ ​

Where,

Q1 is the heat supplied to the hot body.

​

Thermodynamics 15
 Q2 is the heat lost to the cold body.
​

Heat engine will continue its operation till Q1 is greater than Q2 or there is
​ ​

a considerable difference between the temperatures of furnace and the

heat sink.
Efficiency Of Heat Engine:

Q2
%η = (1 − ) x 100 
​

​ ​

Q1 ​

T2
%η = (1 − ) x 100 
​

​ ​

T1​

Smaller the ratio TT21 , greater will be the efficiency of heat engine.
​

​
​

The ratio TT21 can be minimized by decreasing the temperature of cold

​

​
​

body or by increasing the temperature of hot body or simply increasing

the difference of temperatures between the hot and cold bodies.

Internal Combustion Engine:

In an internal combustion engine, the working fluid consists of a
combustible fluid placed inside a cylinder. Four-stroke Diesel and petrol
(gasoline) engines are internal combustion engines.

External Combustion Engine:

In an external combustion engine, the combustion takes place outside the
cylinder. Heat then needs to be transferred to the cylinder where work is
done. Steam engines are example of external combustion engines.

Entropy
“The measure of the disorder of the system is known as entropy of that
system”.
OR
“The measure of unavailability of useful energy is termed as entropy of that
system”.

Thermodynamics 16
 “The change in entropy of the system is equal to the amount of heat
supplied or taken out of the system per unit absolute temperature of
system.”
ΔQ
ΔS = T
​

Here,
ΔS is the change in entropy of system.
ΔQis the amount of heat supplied or taken out.
T is the absolute temperature of the system.
If heat is supplied to a system then change in entropy is positive.

If heat is taken out of the system, change in entropy is negative.

Its unit is J /K .

Second Law Of Thermodynamics For Entropy:

The second law of thermodynamics states that the total entropy of a
system either increases or remains constant in any spontaneous process; it
never decreases.

Practice Questions
1. At constant pressure, the graph between volume (V) and temperature (T) is
:
a) A parabola b) A curve
c) A straight line d) A hyperbola

2. A steam engine has a boiler that operates at 450 K. The heat changes
water to steam, which drives the piston. The exhaust temperature of the
outside air is about 300 K. The maximum efficiency of this steam engine is:
a) 33.3% b) −50%
c) 50% d) 0.33%

3. Heat is a form of energy associated with:

a) Molecular mass b) Molecular weight
c) Molecular motion d) None of these

Thermodynamics 17
 4. Thermostat is a device used to keep the:

a) Temperature constant b) Entropy constant

c) Heat Constant d) Pressure Constant

5. In liquid-in-glass thermometer the thermometric property used is ?

a) Thermal Expansion b) Color Change on heating

c) Both a and b d) None of these

6. Boltzmann constant is written as K =?

a) N
R
 ​ b) NR  ​

A ​

R
c) RNA  ​ d) N  ​

7. Which of the following is correct (w.r.t size of division)?

o o
a) 1 C > 1K  b) 1 C = 1K 
c) 1o C < 1K  d) None of these

8. At constant temperature, if the volume of the given mass of gas is doubled

the density of gas?
a) Remains constant b) Becomes one-fourth
c) Becomes double d) Becomes one-half

9. On Fahrenheit scale the temperature of 50o C will be ?

a) 40o F  b) 50o F 
c) 122o F  d) 105o F 

10. In adiabatic expansion , The internal energy of the gas:

a) Remains same b) Decreases

c) Increases d) Becomes Zero

11. Absolute zero corresponds to this temperature on Fahrenheit scale ?

a) −180o F  b) −40o F 
c) −459.6o F  d) −273.15o F 

Thermodynamics 18
 12. The maximum work done for the same amount of heat is possible in this
process?
a) Isobaric b) Isothermal
c) Isochoric d) None of these

13. The efficiency of Carnot engine depends upon:

a) Sink temperature b) Source temperature

c) Temperature difference of both d) All of these

14. Which of the following relation shows adiabatic process?

a) ΔW = −ΔU  b) ΔW = ΔQ
c) ΔW = ΔU  d) ΔW = 0
15. Which of the following are the processes of transfer of heat?
a) Conduction b) Convection

c) Radiation d) All the above

16. Heat is also called:

a) Energy in stress b) Energy in power
c) Energy in transit d) Energy in elasticity

17. The average kinetic energy of the molecules of a body determines:

a) Heat b) Temperature
c) Internal Energy d) None

18. The linear thermal expansion is related to :

a) Liquids only b) Gases only
c) Solids only d) Both liquids and gases

19. Among hot cup of tea and cold glass of water which carry more heat?

a) Hot cup of tea b) cold glass of water

c) None carries heat d) Incomplete information
given

Thermodynamics 19
 20. A heat engine performs 100 J of work and at the same time rejects 400 J
of heat energy to the cold reservoirs. What is the efficiency of the engine?
a) 11% b) 20%
c) 75% d) 25%

21. Suppose heat is added to a mixture where ice is melted. During the melting
process the temperature of mixture:
a) Remains the same b) Increases
c) Decreases d) Decrease first then
increases

22. The ratio of CP /CV for O2 gas is?

​ ​ ​

a) 1.30 b) 1.50
c) 1.67 d) 1.40

Answer key

1. c 12. b

2. a 13. d

3. c 14. a

4. a 15. d

5. a 16. c

6. b 17. b

7. b 18. c

8. d 19. c

9. c 20. b

10. b 21. a

11. c 22. d

Thermodynamics 20
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Thermodynamics 21