Work done and Heat Transferred

Applying the first law of thermodynamics to the process

dU = dQ - dW

Replacing dW with the reversible work

dU = dQ - PdV

since the volume is constant dV = 0 and

dU = dQ

using the definition of the specific heat at constant volume

to replace dU in the first law

For a constant volume process, the addition or removal of heat will lead to a change in the temperature and pressure of the gas, as shown on the two graphs above

Entropy Change

 To find the Entropy change, start with the expression derived from the first law

dU = dQ

and replace dU using the definition of specific heat at constant volume and dQ using the definition of entropy