Thermodynamics | Physics Optional Notes for UPSC PDF Download

 Page 1


 
 
THERMODYNAMIC ’S 
Thermodynamic System: 
 
A thermodynamic system is a setup involving pressure (P), volume (V), and temperature 
(T). It's a specific portion of matter containing one or more substances where scientists 
study the effects of variables like temperature, volume,, and pressure. This setup allows 
us to analyze and understand how these factors interact and affect the system.. e.g. A gas 
enclosed in a cylinder fitted with a piston is a system. 
 
Surroundings: 
Anything outside the system, which exchanges energy with the system and which tends 
to change the properties of the system is called its surroundings. 
Heterogeneous System: 
A system which is not uniform throughout is said to be heterogeneous. e.g. A system 
consisting of two or more immiscible liquids. 
Homogeneous System: 
A system is said to be homogeneous if it is completely uniform throughout. e.g. Pure 
solid or liquid. 
Isolated System: 
A system in which there can be no exchange of matter and energy with the surroundings 
is said to be an isolated system. 
Universe: 
The system and its surroundings are together known as the universe. 
Thermodynamic variables of the System:  
(i) Composition (?? ) 
Page 2


 
 
THERMODYNAMIC ’S 
Thermodynamic System: 
 
A thermodynamic system is a setup involving pressure (P), volume (V), and temperature 
(T). It's a specific portion of matter containing one or more substances where scientists 
study the effects of variables like temperature, volume,, and pressure. This setup allows 
us to analyze and understand how these factors interact and affect the system.. e.g. A gas 
enclosed in a cylinder fitted with a piston is a system. 
 
Surroundings: 
Anything outside the system, which exchanges energy with the system and which tends 
to change the properties of the system is called its surroundings. 
Heterogeneous System: 
A system which is not uniform throughout is said to be heterogeneous. e.g. A system 
consisting of two or more immiscible liquids. 
Homogeneous System: 
A system is said to be homogeneous if it is completely uniform throughout. e.g. Pure 
solid or liquid. 
Isolated System: 
A system in which there can be no exchange of matter and energy with the surroundings 
is said to be an isolated system. 
Universe: 
The system and its surroundings are together known as the universe. 
Thermodynamic variables of the System:  
(i) Composition (?? ) 
(ii) Temperature ( T ) 
(iii) Volume (V) 
(iv) Pressure (P) 
(v) Mass 
Thermodynamic state: 
 
The condition of a system can be fully explained by its makeup, temperature, volume, 
and pressure. If a system is uniform and has a fixed mass and composition, then its 
condition can be determined by just three variables: temperature, pressure, and volume. 
These three factors together provide a comprehensive description of the system's state. 
These variables are interrelated by equation PV= ?? RT The thermodynamic state of the 
system is its condition as identified by two independent thermodynamic variables ( P,V 
or P,T or V,T ). 
- Zeroth law of Thermodynamics 
If two objects, let's call them A and B, are both in thermal equilibrium with a third 
object, say C (like a thermometer), then A and B are also in thermal equilibrium with 
each other. This concept is introduced by the zeroth law of thermodynamics, which is 
about temperature. When two objects or systems have the same temperature, we say 
they are in thermal equilibrium. This means that they are at the same level of "hotness" 
or "coldness" and no heat flows between them when they are in contact. 
{Note: In measuring the temperature of a body, it is important that the thermometer be 
in the thermal equilibrium with the body whose temperature is to be measured.} 
C 
A B 
 
Thermal Equilibrium: 
Thermal equilibrium is a situation in which two objects in thermal contact cease to 
exchange energy by the process of heat. Heat is the transfer of energy from one object to 
another object as a result of a difference in temperature between them. 
Work done by Gas: 
Let ’s consider a cylinder of area An enclosed with the moveable piston. If the gas 
enclosed is at pressure P, then force applied by the gas on the piston is F. 
?? = ???? 
Page 3


 
 
THERMODYNAMIC ’S 
Thermodynamic System: 
 
A thermodynamic system is a setup involving pressure (P), volume (V), and temperature 
(T). It's a specific portion of matter containing one or more substances where scientists 
study the effects of variables like temperature, volume,, and pressure. This setup allows 
us to analyze and understand how these factors interact and affect the system.. e.g. A gas 
enclosed in a cylinder fitted with a piston is a system. 
 
Surroundings: 
Anything outside the system, which exchanges energy with the system and which tends 
to change the properties of the system is called its surroundings. 
Heterogeneous System: 
A system which is not uniform throughout is said to be heterogeneous. e.g. A system 
consisting of two or more immiscible liquids. 
Homogeneous System: 
A system is said to be homogeneous if it is completely uniform throughout. e.g. Pure 
solid or liquid. 
Isolated System: 
A system in which there can be no exchange of matter and energy with the surroundings 
is said to be an isolated system. 
Universe: 
The system and its surroundings are together known as the universe. 
Thermodynamic variables of the System:  
(i) Composition (?? ) 
(ii) Temperature ( T ) 
(iii) Volume (V) 
(iv) Pressure (P) 
(v) Mass 
Thermodynamic state: 
 
The condition of a system can be fully explained by its makeup, temperature, volume, 
and pressure. If a system is uniform and has a fixed mass and composition, then its 
condition can be determined by just three variables: temperature, pressure, and volume. 
These three factors together provide a comprehensive description of the system's state. 
These variables are interrelated by equation PV= ?? RT The thermodynamic state of the 
system is its condition as identified by two independent thermodynamic variables ( P,V 
or P,T or V,T ). 
- Zeroth law of Thermodynamics 
If two objects, let's call them A and B, are both in thermal equilibrium with a third 
object, say C (like a thermometer), then A and B are also in thermal equilibrium with 
each other. This concept is introduced by the zeroth law of thermodynamics, which is 
about temperature. When two objects or systems have the same temperature, we say 
they are in thermal equilibrium. This means that they are at the same level of "hotness" 
or "coldness" and no heat flows between them when they are in contact. 
{Note: In measuring the temperature of a body, it is important that the thermometer be 
in the thermal equilibrium with the body whose temperature is to be measured.} 
C 
A B 
 
Thermal Equilibrium: 
Thermal equilibrium is a situation in which two objects in thermal contact cease to 
exchange energy by the process of heat. Heat is the transfer of energy from one object to 
another object as a result of a difference in temperature between them. 
Work done by Gas: 
Let ’s consider a cylinder of area An enclosed with the moveable piston. If the gas 
enclosed is at pressure P, then force applied by the gas on the piston is F. 
?? = ???? 
 
Not if the piston moves towards right a dx distance then work done by this force is d?? . 
d?? = F · dx 
= ?? (?? · ???? ) 
d?? = PdV 
d?? = ?
?? 1
?? 2
??????? 
If the gas expands against the piston: 
 
Gas exerts a force on the piston and displace it through a distance and gas does work on 
the piston. 
If the piston compresses the gas : 
When piston moved inward, work is done on the gas. 
WORK CALCULATION FOR DIFFERENT PROCESS ISOMETRIC OR 
ISOCHORIC PROCESS 
? Isochoric process is a thermodynamic process that takes place at constant volume 
of the system, but pressure and temperature varies for change in state of the 
system. 
Equation of state: P = constant × T(P and T are variable, V is constant ) 
Work done: In this process volume remains constant ??? = 0 or dV= 0 
W= ?
?? ?? ?? ?? ?PdV= 0 
ISOTHERMAL PROCESS 
In this process pressure and volume of system change but temperature remains constant. 
In an isothermal process, the exchange of heat between the system and the surroundings 
Page 4


 
 
THERMODYNAMIC ’S 
Thermodynamic System: 
 
A thermodynamic system is a setup involving pressure (P), volume (V), and temperature 
(T). It's a specific portion of matter containing one or more substances where scientists 
study the effects of variables like temperature, volume,, and pressure. This setup allows 
us to analyze and understand how these factors interact and affect the system.. e.g. A gas 
enclosed in a cylinder fitted with a piston is a system. 
 
Surroundings: 
Anything outside the system, which exchanges energy with the system and which tends 
to change the properties of the system is called its surroundings. 
Heterogeneous System: 
A system which is not uniform throughout is said to be heterogeneous. e.g. A system 
consisting of two or more immiscible liquids. 
Homogeneous System: 
A system is said to be homogeneous if it is completely uniform throughout. e.g. Pure 
solid or liquid. 
Isolated System: 
A system in which there can be no exchange of matter and energy with the surroundings 
is said to be an isolated system. 
Universe: 
The system and its surroundings are together known as the universe. 
Thermodynamic variables of the System:  
(i) Composition (?? ) 
(ii) Temperature ( T ) 
(iii) Volume (V) 
(iv) Pressure (P) 
(v) Mass 
Thermodynamic state: 
 
The condition of a system can be fully explained by its makeup, temperature, volume, 
and pressure. If a system is uniform and has a fixed mass and composition, then its 
condition can be determined by just three variables: temperature, pressure, and volume. 
These three factors together provide a comprehensive description of the system's state. 
These variables are interrelated by equation PV= ?? RT The thermodynamic state of the 
system is its condition as identified by two independent thermodynamic variables ( P,V 
or P,T or V,T ). 
- Zeroth law of Thermodynamics 
If two objects, let's call them A and B, are both in thermal equilibrium with a third 
object, say C (like a thermometer), then A and B are also in thermal equilibrium with 
each other. This concept is introduced by the zeroth law of thermodynamics, which is 
about temperature. When two objects or systems have the same temperature, we say 
they are in thermal equilibrium. This means that they are at the same level of "hotness" 
or "coldness" and no heat flows between them when they are in contact. 
{Note: In measuring the temperature of a body, it is important that the thermometer be 
in the thermal equilibrium with the body whose temperature is to be measured.} 
C 
A B 
 
Thermal Equilibrium: 
Thermal equilibrium is a situation in which two objects in thermal contact cease to 
exchange energy by the process of heat. Heat is the transfer of energy from one object to 
another object as a result of a difference in temperature between them. 
Work done by Gas: 
Let ’s consider a cylinder of area An enclosed with the moveable piston. If the gas 
enclosed is at pressure P, then force applied by the gas on the piston is F. 
?? = ???? 
 
Not if the piston moves towards right a dx distance then work done by this force is d?? . 
d?? = F · dx 
= ?? (?? · ???? ) 
d?? = PdV 
d?? = ?
?? 1
?? 2
??????? 
If the gas expands against the piston: 
 
Gas exerts a force on the piston and displace it through a distance and gas does work on 
the piston. 
If the piston compresses the gas : 
When piston moved inward, work is done on the gas. 
WORK CALCULATION FOR DIFFERENT PROCESS ISOMETRIC OR 
ISOCHORIC PROCESS 
? Isochoric process is a thermodynamic process that takes place at constant volume 
of the system, but pressure and temperature varies for change in state of the 
system. 
Equation of state: P = constant × T(P and T are variable, V is constant ) 
Work done: In this process volume remains constant ??? = 0 or dV= 0 
W= ?
?? ?? ?? ?? ?PdV= 0 
ISOTHERMAL PROCESS 
In this process pressure and volume of system change but temperature remains constant. 
In an isothermal process, the exchange of heat between the system and the surroundings 
is allowed. Isothermal process is carried out by either supplying heat to the substance or 
by extracting heat from it. A process has to be extremely slow to be isothermal. 
Equation of state: 
???? = constant ( ?????? )(?? is constant ) 
Work Done: 
Consider n moles of an ideal gas, enclosed in a cylinder, at absolute temperatureT, fitted 
with a frictionless piston. Suppose that gas undergoes an isothermal expansion from the 
initial state (P
1
, V
1
) to the final state (P
2
, V
2
) . 
?  Work done: ?? = ?
?? 1
?? 2
?
?????? ?? ???? = ?????? ?
?? 1
?? 2
?
????
?? = ?????? [log
?? ?? ?? 1
?? 2
 
 = nRT [log
e
 V
2
- log
e
 V
1
] = nRT log
?? [
V
2
 V
1
]
? W = 2.303?? RTlog
10
 [
P
1
P
2
][? P
1
 V
1
= P
2
 V
2
]
 
ISOBARIC PROCESS 
Isobaric process is a thermodynamic process that takes place at constant pressure, but 
volume and temperature varies for change in state of the system. 
? Equation of state 
V = Constant × T or V ? T 
? Work done 
In this process pressure remains constant  ?P = 0 
Work done ?? = ?
?? ?? ?? ?? ??????? = ?? (?? ?? - ?? ?? ) 
POLYTROPHIC PROCESS: 
When P and V bear the relation PV
x
= constant, where x ? 1 or ?? the process is called a 
polytropic one. 
??? = ? ?
?? ?? ?? ??????? = ? ?
?? ?? ?? ??? ?? -?? ???? = [
?? ?? -?? -1
-?? + 1
]
?? ?? ?? =
?? ?? ?? -?? +1
- ?? ?? ?? -?? +1
-?? + 1
=
?? ?? ?? ?? ?? ?? ?? -?? +1
- ?? ?? ?? ?? ?? ?? ?? -?? +1
1 - ?? =
?? ?? ?? ?? - ?? ?? ?? ?? 1 - ?? =
???? [?? ?? - ?? ?? ]
1 - ?? =
???? ??? 1 - ?? [???? = ?????? ]
 
Page 5


 
 
THERMODYNAMIC ’S 
Thermodynamic System: 
 
A thermodynamic system is a setup involving pressure (P), volume (V), and temperature 
(T). It's a specific portion of matter containing one or more substances where scientists 
study the effects of variables like temperature, volume,, and pressure. This setup allows 
us to analyze and understand how these factors interact and affect the system.. e.g. A gas 
enclosed in a cylinder fitted with a piston is a system. 
 
Surroundings: 
Anything outside the system, which exchanges energy with the system and which tends 
to change the properties of the system is called its surroundings. 
Heterogeneous System: 
A system which is not uniform throughout is said to be heterogeneous. e.g. A system 
consisting of two or more immiscible liquids. 
Homogeneous System: 
A system is said to be homogeneous if it is completely uniform throughout. e.g. Pure 
solid or liquid. 
Isolated System: 
A system in which there can be no exchange of matter and energy with the surroundings 
is said to be an isolated system. 
Universe: 
The system and its surroundings are together known as the universe. 
Thermodynamic variables of the System:  
(i) Composition (?? ) 
(ii) Temperature ( T ) 
(iii) Volume (V) 
(iv) Pressure (P) 
(v) Mass 
Thermodynamic state: 
 
The condition of a system can be fully explained by its makeup, temperature, volume, 
and pressure. If a system is uniform and has a fixed mass and composition, then its 
condition can be determined by just three variables: temperature, pressure, and volume. 
These three factors together provide a comprehensive description of the system's state. 
These variables are interrelated by equation PV= ?? RT The thermodynamic state of the 
system is its condition as identified by two independent thermodynamic variables ( P,V 
or P,T or V,T ). 
- Zeroth law of Thermodynamics 
If two objects, let's call them A and B, are both in thermal equilibrium with a third 
object, say C (like a thermometer), then A and B are also in thermal equilibrium with 
each other. This concept is introduced by the zeroth law of thermodynamics, which is 
about temperature. When two objects or systems have the same temperature, we say 
they are in thermal equilibrium. This means that they are at the same level of "hotness" 
or "coldness" and no heat flows between them when they are in contact. 
{Note: In measuring the temperature of a body, it is important that the thermometer be 
in the thermal equilibrium with the body whose temperature is to be measured.} 
C 
A B 
 
Thermal Equilibrium: 
Thermal equilibrium is a situation in which two objects in thermal contact cease to 
exchange energy by the process of heat. Heat is the transfer of energy from one object to 
another object as a result of a difference in temperature between them. 
Work done by Gas: 
Let ’s consider a cylinder of area An enclosed with the moveable piston. If the gas 
enclosed is at pressure P, then force applied by the gas on the piston is F. 
?? = ???? 
 
Not if the piston moves towards right a dx distance then work done by this force is d?? . 
d?? = F · dx 
= ?? (?? · ???? ) 
d?? = PdV 
d?? = ?
?? 1
?? 2
??????? 
If the gas expands against the piston: 
 
Gas exerts a force on the piston and displace it through a distance and gas does work on 
the piston. 
If the piston compresses the gas : 
When piston moved inward, work is done on the gas. 
WORK CALCULATION FOR DIFFERENT PROCESS ISOMETRIC OR 
ISOCHORIC PROCESS 
? Isochoric process is a thermodynamic process that takes place at constant volume 
of the system, but pressure and temperature varies for change in state of the 
system. 
Equation of state: P = constant × T(P and T are variable, V is constant ) 
Work done: In this process volume remains constant ??? = 0 or dV= 0 
W= ?
?? ?? ?? ?? ?PdV= 0 
ISOTHERMAL PROCESS 
In this process pressure and volume of system change but temperature remains constant. 
In an isothermal process, the exchange of heat between the system and the surroundings 
is allowed. Isothermal process is carried out by either supplying heat to the substance or 
by extracting heat from it. A process has to be extremely slow to be isothermal. 
Equation of state: 
???? = constant ( ?????? )(?? is constant ) 
Work Done: 
Consider n moles of an ideal gas, enclosed in a cylinder, at absolute temperatureT, fitted 
with a frictionless piston. Suppose that gas undergoes an isothermal expansion from the 
initial state (P
1
, V
1
) to the final state (P
2
, V
2
) . 
?  Work done: ?? = ?
?? 1
?? 2
?
?????? ?? ???? = ?????? ?
?? 1
?? 2
?
????
?? = ?????? [log
?? ?? ?? 1
?? 2
 
 = nRT [log
e
 V
2
- log
e
 V
1
] = nRT log
?? [
V
2
 V
1
]
? W = 2.303?? RTlog
10
 [
P
1
P
2
][? P
1
 V
1
= P
2
 V
2
]
 
ISOBARIC PROCESS 
Isobaric process is a thermodynamic process that takes place at constant pressure, but 
volume and temperature varies for change in state of the system. 
? Equation of state 
V = Constant × T or V ? T 
? Work done 
In this process pressure remains constant  ?P = 0 
Work done ?? = ?
?? ?? ?? ?? ??????? = ?? (?? ?? - ?? ?? ) 
POLYTROPHIC PROCESS: 
When P and V bear the relation PV
x
= constant, where x ? 1 or ?? the process is called a 
polytropic one. 
??? = ? ?
?? ?? ?? ??????? = ? ?
?? ?? ?? ??? ?? -?? ???? = [
?? ?? -?? -1
-?? + 1
]
?? ?? ?? =
?? ?? ?? -?? +1
- ?? ?? ?? -?? +1
-?? + 1
=
?? ?? ?? ?? ?? ?? ?? -?? +1
- ?? ?? ?? ?? ?? ?? ?? -?? +1
1 - ?? =
?? ?? ?? ?? - ?? ?? ?? ?? 1 - ?? =
???? [?? ?? - ?? ?? ]
1 - ?? =
???? ??? 1 - ?? [???? = ?????? ]
 
Graphical interpretation of Thermodynamically work done: 
From the above integral it can be understood that the area enclosed by the PV-curve and 
the V-axis represents the work done by gas. 
(i) 
 
(ii) 
 
When volume increases ??? is +ve 
(iii) 
 
When volume decrease ??? is --ve (iv) 
 
When volume decrease ??? is - ve