#### Question

Write mathematical equation of first law of thermodynamics for Isochoric process

#### Solution

By substituting equation `W= -p_(ex).triangleV` in the equation `triangleU=q+W`, we get

`triangleU=q-p_(ex).triangleV .........(1)`

If the reaction is carried out in a closed container so that the volume of the system is constant, then`triangleV=0.`In such a case, no work is involved.

The equation (1) becomes `triangleU=q_v.`

Equation (1) suggests that the change in internal energy of the system is due to heat transfer. The subscript v indicates a constant volume process. As U is a state function, qv is also a state function. We see that an increase in the internal energy of a system is numerically equal to the heat absorbed by the system in a constant volume (isochoric) process.