Question

An ideal gas having molar specific heat at constant volume C_V. It is undergoing a process where temperature is varying as T = T₀e^aV where a is constant and 'V' is the volume occupied by the gas. The molar specific heat of the gas for the given process as a function of volume is given by:

• A. C_V +$\frac{\alpha R}{V}$
• B. C_V +$\frac{R}{\alpha V}$
• C. C_V +$\frac{2\alpha R}{V}$
• D. C_V +$\frac{R}{2\alpha V}$

Answer 1

Answer: (B)

C_V +$\frac{R}{\alpha V}$

Answer 2

From 1^st law,

DQ = DU + W

nCdT = nC_VdT + pdV

Ž nCdT = nC_VdT +$\frac{nRT}{V}$ dV

Ž CaT₀e^aVdV= C_V aT₀e^aVdV+$\frac{nR}{V}$T₀e^aV dV

Ž aC = aC_V +$\frac{R}{V}$

Ž C = C_V +$\frac{R}{\alpha V}$