Question

By applying the first law of thermodynamics to isobaric process. Obtain relation between two specific heats of a gas.

Answer 1

In an isobaric process, pressure remains constant. If an amount of heat dQ is supplied to one mole of a gas at constant pressure and its temperature increases by dT, then

dQ = C_pdT

Here C_p is molar specific heat of the gas at constant pressure. Therefore, for an isobaric process, the first law of thermodynamics becomes :

C_pdt = dU + PdV …(i)

From perfect gas equation it follows that

PdV = RdT

In the eqn. (i), substituting PdV and dU, we have

C_PdT = C_vdT+ RdT

C_p = C_v+ R.