Constant Volume Process (Isochoric Process)

When the gas is heated at a constant volume, its temperature and pressure will be increased. Since there is no changes in its volume, no external work is done by the gas. All the heat supplied is stored in the body of the gas in the form of internal energy.

Consider that m Kg of a certain gas being heated at a constant volume from an initial temperature T₁ to final temperature T₂. This process is shown on the P-V diagram.

It may be noted that the area below the P-V diagram of a thermodynamic process represents the work done during the process to same scale.

We know that, Heat Supplied

                        Q_1-2 = (U₂-U₁)+W_1-2                              W_1-2=0

                                 = U₂-U₁

We also know that, the internal energy,

                                 U₂-U₁= mC_v (T₂-T₁)

Heat supplied,          Q_1-2 = mC_v (T₂-T₁)

So, Heat supplied to the gas at constant volume = Mass X Specific heat at constant volume X Rise in temperature.