__What is called a Thermodynamic Process?__

*A process in which at least two or more state variables of a system got change, is called a thermodynamic process.*

For example – Consider that, in a piston cylinder arrangement, pressure of a certain quantity of gas is increases by pressing the piston slowly, while the temperature of the gas is maintained constant.

In this compression process –

- Pressure of the gas has changed and increases.
- Volume of the gas has changed and decreases.
- Temperature of the gas is unchanged and remains constant.

Pressure and volume both are the state functions which has got changed. Hence, the above process is a thermodynamic process.

Different thermodynamic process which are important for the subject of consideration are as follows –

- Isochoric process or Isometric process.
- Isobaric process or Isopiestic process.
- Isothermal or Isotropic process.
- Adiabatic process.

These processes are explained as follows –

__Isochoric or Isometric Process__

*A thermodynamic process in which the volume of system remains constant is called an isochoric or isometric process.*

The equation of state for an isochoric process is –

V = \text {Constant}

So, change in volume of the system is zero i.e. \Delta V = 0

Therefore, \Delta W = P \Delta V = P \times 0 = 0

- Hence, work done in an isochoric process us zero.

From *first law of thermodynamics*, we get –

\Delta Q = \Delta U + \Delta W

Or, \quad \Delta Q = \Delta U + 0 = \Delta U

*Hence, in an isochoric process, the entire heat change used to change the internal energy of the system due to change in its temperature.*

The change in temperature can be determined by the equation –

Q = n C_V \ \Delta T

__Isobaric or Isopiestic Process__

*A thermodynamic process which occurs at constant pressure is called an isobaric or isopiestic process.*

- In isobaric process the volume and temperature of the system change but the pressure remains constant.
- The equation of state for an isobaric process is –

P = \text {Constant}

*An isochoric process strictly obeys Charle’s law.*

__Work Done in Isobaric Process__

Suppose, a gas expands at constant pressure from initial state ( V_1, \ T_1 ) to final state ( V_2, \ T_2 )

- Amount of work done by the gas will be –

W_{isobaric} = \int\limits_{V_1}^{V_2} P dV

Or, \quad W_{isobaric} = P \int\limits_{V_1}^{V_2} dV

= P \left ( V_2 - V_1 \right ) = n R \left ( T_2 - T_1 \right )

- Therefore, work done in an isobaric process is given by –

W_{isobaric} = n R \left ( T_2 - T_1 \right ) ……….. (1)

__Isothermal or Isotropic Process__

*An isothermal process is a thermodynamic process in which the process occurs at constant temperature conditions. It is also called an isotropic process.*

- In isothermal process, the pressure and volume of the system change but the temperature remains constant.
- The boundary of the system is consisting of conducting walls so that it allows flow of heat to maintain the system temperature constant.
- The process occur very slowly so as to provide sufficient time for the exchange of heat from
*system*to*surrounding*or vice versa.

The equation of state for an ** isothermal process** is –

PV = Constant.

Therefore, \quad P_1 V_1 = P_2 V_2

*An isothermal process strictly obeys Boyle’s law.*

__Work Done in Isothermal Process__

Consider ( n ) moles of an *ideal gas* contained in a cylinder of cross sectional area *A *and having conducting walls and friction-less piston as shown in figure.

When piston moves up through a small distance ( dx ) ,* *the work done will be –

\Delta W = P A dx = P dV

Then total amount of work done by the gas, when it expands isothermally from initial state ( P_1, \ V_1 ) to final state ( P_2, \ V_2 ) will be –

W_{iso} = \int\limits_{V_1}^{V_2} P dV

But, for ( n ) moles of a gas –

P V = n R T

Or, \quad P = \left ( \frac { n R T }{ V } \right )

Therefore, \quad W_{iso} = \int\limits_{V_1}^{V_2} \left ( \frac { n R T }{ V } \right ) dV

= n R T \int\limits_{V_1}^{V_2} \left ( \frac {1}{V} \right ) dV

= n R T \left [ \ln V_2 - \ln V_1 \right ]

= n R T \ln \left ( \frac {V_2}{V_1} \right )

But, \quad P_1 V_1 = P_2 V_2

Therefore, \quad W_{iso} = 2.303 \ n R T \log \left ( \frac {V_2}{V_1} \right )

= 2.303 \ n R T \log \left ( \frac {P_1}{P_2} \right )

Therefore, work done in an isothermal process is given by –

W_{iso} = 2.303 \ n R T \log \left ( \frac {V_2}{V_1} \right ) ……… (2)

= 2.303 \ n R T \log \left ( \frac {P_1}{P_2} \right ) ………. (3)

__Adiabatic Process__

*An adiabatic process is a thermodynamic process in which the process occurs without exchange of heat from surroundings.*

- In an adiabatic process pressure, volume and temperature of the system change but heat exchange not occur.
- The boundary of the system consisting of non-conducting walls so that it doesn’t allows flow of heat to and from surroundings.
- The process should occur very fast so that heat does not get enough time for the exchange from system to surrounding or vice versa.

__Work Done in Adiabatic Process__

Consider ( n ) moles of an ideal gas contained in a cylinder of cross sectional area ( A ) * *and having perfectly insulated walls and friction-less piston as shown in figure.

Suppose, the gas expands adiabatically from initial state ( P_1, \ V_1, \ T_1 ) to final state ( P_2, \ V_2, \ T_2 )

Total work done by the gas will be –

W_{adia} = \int\limits_{V_1}^{V_2} P dV

But, for an ideal gas in adiabatic process –

P V^{\gamma} = \text {Constant}

Or, \quad P = K V^{- \gamma}

Therefore, work done in an adiabatic process –

W_{adia} = \int\limits_{V_1}^{V_2} KV^{- \gamma} dV= K \int\limits_{V_1}^{V_2} V^{- \gamma} dV

= K \left [ \frac { V^{ 1 - \gamma }}{ 1 - \gamma } \right ]_{V_1}^{V_2}

= \left ( \frac {K}{1 - \gamma} \right ) \left [ V^{1 - \gamma}_{2} - V^{1 - \gamma}_{1} \right ]

But, \quad P_1V^{\gamma}_1 = P_2V^{\gamma}_2 = K

Therefore, \quad W_{adia} = \left ( \frac {1}{1 - \gamma} \right ) \left [ P_2V_2V^{1 - \gamma}_{2} - P_1V_1V^{1 - \gamma}_{1} \right ]

= \left ( \frac {1}{1 - \gamma} \right ) \left [ P_2V_2 - P_1V_1 \right ]

= \left ( \frac {1}{\gamma - 1} \right ) \left [ P_1V_1 - P_2V_2 \right ]

Also, \quad P_1V_1 = n R T_1 \quad and \quad P_2V_2 = n R T_2

Therefore, \quad W_{adia} = \left ( \frac {1}{\gamma - 1} \right ) \left [ nRT_1 - nRT_2 \right ]

= \left ( \frac {nR}{\gamma - 1} \right ) \left [ T_1 - T_2 \right ]

Therefore, work done in an adiabatic process is given by –

W_{adia} = \left ( \frac {1}{\gamma - 1} \right ) \left [ P_1V_1 - P_2V_2 \right ] ……… (4)

= \left ( \frac {nR}{\gamma - 1} \right ) \left [ T_1 - T_2 \right ] …….. (5)

__PV, PT & VT Diagrams__

For better understanding of difference between curves relating to ( P ), \ ( V ) and ( T ) in thermodynamic processes we have plotted on the same axes as shown below. These are –

- Pressure verses Volume diagram.
- Pressure verses Temperature diagram.
- Volume verses Temperature diagram.

These diagrams are explained as below –

### Pressure-Volume Diagram

Figure shows Pressure-Volume diagram of expansion of a gas.

- Blue colored curve indicates PV diagram of an isobaric process. It is a straight line parallel to the volume axis.
- Green colored curve indicates PV diagram of an isothermal process. It is a curve of increasing slope.
- Red colored curve indicates PV diagram of an adiabatic process. It is a curve of increasing slope.
- Orange colored curve indicates PV diagram of an isochoric process. It is a straight line parallel to pressure axis.

### Pressure-Temperature Diagram

Figure shows Pressure-Temperature diagram of expansion of a gas.

- Blue colored curve indicates PT diagram of an isobaric process. It is a straight line parallel to the temperature axis.
- Green colored curve indicates PT diagram of an isothermal process. It is a straight line parallel to the pressure axis.
- Red colored curve indicates PT diagram of an adiabatic process. It is curve with decreasing slope.
- Orange colored curve indicates PT diagram of an isochoric process. It is a slanting straight line with constant slope.

### Volume-Temperature Diagram

Figure shows Volume-Temperature diagram of expansion of a gas.

- Blue colored curve indicates VT diagram of an isobaric process.
- It is a slanting straight line with constant slope.
- Green colored curve indicates VT diagram of an isothermal process. It is a straight line parallel to the volume axis.
- Red colored curve indicates VT diagram of an adiabatic process.
- It is a curve of decreasing slope.
- Orange colored curve indicates VT diagram of an isochoric process. It is a straight line parallel to temperature axis.

See numerical problems based on this article.