(a) Prove that for a monatomic gas the ratio of molar specific heat at constant pressure to molar specific heat at constant volume is $1.67.$
(b) Is it possible to boil water without heating? Explain.

If $\mathrm{Cp} \mathrm{and} \mathrm{Cv}$ denotes the specific heats of nitrogen per unit-mass at constant pressure and constant volume respectively, then :

Two samples of $A$ and $B$ are initially kept in the same state. The sample $A$ is expanded through an adiabatic process and the sample $B$ through an isothermal process up to the same final volume. The final pressures in $A$ and $B$ are $P_{\mathrm{A}}$ and $P_{\mathrm{B}}$ respectively. Then,

Four curves $A, B, C$ and $D$ are drawn in the figure for a given amount of gas. The curves which represent adiabatic and isothermal changes are