Question

An ideal gas is taken through a process in which the pressure and the volume are changed according to the equation P = kV. Molar heat capacity of the gas for the process is(a) $C=C_{V}+R$(b) $C=C_{V}+\frac{R}{2}$(c) $C=C_{V}-\frac{R}{2}$(d) $C=C_{V}+R$

Answer 1

Relation between pressure and volume of a gas is P = kV.

Ideal gas equation will be PV = nRT.

= nRTV=kV    ⇒nRT=kV2

For simplicity, we will take the number of moles of  a gas, n = 1.

= RdT = 2 kVdV

= RdT2kV=dV

From the first law of thermodynamics,

dQ = dU + dW

=nCpdT = Cv dT + PdV

= nCpdT = Cv dT+PRdT2kV⇒1×Cp

= Cv+PR2kV

Therefore, the molar heat capacity of the gas for the process is Cp=Cv+R2