Constant volume process | Isochoric process

A constant volume process is also called the isochoric process, an isovolumetric process is one type of thermodynamic process during the volume of a closed system is constant. The term isochoric is derived from the Greek word 'ISO' means constant or equal and 'CHORIC' means space or volume. 

What is the constant volume isochoric process?

When the gas is heated at constant volume, its pressure and temperature will increase. Since we take volume constant no change in volume, thus no external work is done by the gas. All the heat supplied is stored in the body of gas in the form of internal energy. This process is governed by Gay-Lussac Law. 

Thus, Isochoric process is one in which 

V_f = V_i ( ∆V =  0 dv = 0)

Example of Isochoric process: 

The gas is heated in a closed cylinder is an example of the isochoric process. 

Theoretical explanation:

PV diagram for an isochoric process

Now, from the above figure m kg of gas being heated at a constant volume from an initial temperature T1 to final temperature T2. This process is represented in the P-V diagram in the above figure. 

Now, we know that 

Q_1-2 = (U₂-U₁) + W_1-2 = U₂-U₁

We also know that internal energy, 

U₂-U₁ = m Cv ( T₂-T₁)

So, heat supplied Q_1-2 = (U₂-U₁) = m Cv (T₂-T₁)

Now, in this process, we have shown above dv = 0

Therefore, work done W = ^Vf∫_Vi Pdv = 0

If the change in pressure is positive or negative, the work done by the gas in the isochoric process is zero. 

Thus, work done by the gas in a process in which PVⁿ = Constant. Where n is also constant.