The specific heat at constant pressure of a real gas obeying PV^2 = RT equation is : (1) Cv + R (2) R/3 + Cv (3) R

Question

The specific heat at constant pressure of a real gas obeying PV² = RT equation is :

(1) \(C_{V}+R\)

(2) \(\frac{R}{3}+C_{V}\)

(3) R

(4) \(C_{V}+\frac{R}{2 V}\)

Answer 1

Correct option is : (4) \( C_{V}+\frac{R}{2 V}\)

\(\mathrm{dQ}=\mathrm{du}+\mathrm{dW}\)

\(\mathrm{CdT}=\mathrm{C}_{\mathrm{V}} \mathrm{dT}+\mathrm{PdV}\)     ...........(1)

\(\therefore\ \ \mathrm{PV}^{2}=\mathrm{RT}\)

\(\mathrm{P}=\) constant

\(\mathrm{P}(2 \mathrm{VdV})=\mathrm{RdT}\)

\(\mathrm{PdV}=\frac{\mathrm{RdT}}{2 \mathrm{V}}\)

Put in equation (1)

\( \mathrm{C}=\mathrm{C}_{\mathrm{V}}+\frac{\mathrm{R}}{2 \mathrm{V}} \)