A carnot engine having an efficiency of  as heat engine, is used as a refrigerator. If the work done on the system is $10 \,J,$ the amount of energy absorbed from the reservoir at lower temperature is .......... $\mathrm{J}$

Heat is supplied to a di-atomic gas at constant pressure. The ratio of $\Delta Q : \Delta U : \Delta W$ is

Which of the following graphs correctly represents the variation of $\beta  =  - \left( {\frac{{dV}}{{dP}}} \right)/V$ with $P$ for an ideal gas at constant temperature ?

The coefficient of apparent expansion of mercury in a glass vessel is $153 \times 10^{-6}/\,^oC$ and in a steel vessel is $144 \times 10^{-6}/\,^oC$. If $\alpha $ for steel is $12 \times 10^{-6}/\,^oC$, then $\alpha $ that of glass is

In an adiabatic change, the pressure and temperature of a monoatomic gas are related as $P  \propto  T^C$, where $C$ equals

An ideal gas expands isothermally from a volume $V_1$ to $V_2$ and then compressed to original volume $V_1$ adiabatically. Initial pressure is $P_1$ and final pressure is $P_3$. The total work done is $W$. Then