The expression, nRT In $$\frac{{{{\text{P}}_1}}}{{{{\text{P}}_2}}}$$, is for the ____ of an ideal gas.

A. Compressibility

B. Work done under adiabatic contition

C. Work done under isothermal condition

D. Co-efficient of thermal expansion

Answer: Option C

Solution(By Examveda Team)

Since, the expansion work is equal to $$\delta w = PdV$$
Since for an ideal gas
$$\eqalign{ & PV = nRT \cr & \Rightarrow w = \int {\frac{{nRT}}{V}} dV \cr & \Rightarrow w = nRT\ln \left( {\frac{{{P_1}}}{{{P_2}}}} \right) \cr} $$
(hence for an ideal gas under isothermal conditions)