Question

The figure shows a process on a gas in which pressure and volume both change. The molar heat capacity for this process is C.

विकल्प

• C = 0

•  C = C_v

• C > C_v

•  C < C_v

Answer 1

C > C_​v

Consider two processes AB and ACB; let W be the work done. C is the molar heat capacity of process AB. Process ACB can be considered as the sum of the two processes, AC and CB. The molar heat capacity of process AC is C_p, as pressure is constant in this process and the molar heat capacity of process CB is C_v, as volume is constant in it. 
Internal energy, U, is a state function, i.e. it doesn't depend on the path followed. Therefore,

U_AB = U_ACB

W_AB > W_ACB

Work done in the p-V diagram is the area enclosed under the curve.

⇒ W_AB + U_AB > W_ACB + U_ACB

⇒ C > C_V + C_P

Molar heat capacity is the heat supplied per mole to change the temperature by a degree Kelvin and according to the first law of thermodynamics, dQ = dU + dW, where dQ is the heat supplied to the system in a process.

⇒ C > C_V