Question

Derive the value of molar heat capacity as constant volume.

Answer 1

According to the first law of thermodynamics,

dq = dU + PdV

Dividing both sides by dT, we have

dq / dT = (du + PdV) / dT

At constant volume dV = 0, then

dq / dT = (dU / dT) V

C_v = (dU / dT) v

Thus the heat capacity ai constant volume (C_v) is defined as the rate of change of internal energy with respect to temperature at constant volume.