Constant volume (isochoric) process

Constant volume process or isochoric process - When the gas is heated at a constant volume, its temperature and pressure will increase. Since there is no change 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. It may be noted that this process is governed by Gay-Lussac law.                 

Now consider m kg of a certain gas being heated at a constant volume from an initial temperature T1 to final temperatuire T2. This process is shown on the p-v (i.e. pressure-volume)* diagram in Fig. 5.1

*It may be noted that the area below the p—v diagram of a thermodynamic process represents the work done during the process to some scale.

We know that

We also know that the internal energy,