Two Carnot engines $A$ and $B$ are operated in series. The engine $A$ receives heat from the source at temperature $T_1$ and rejects the heat to the sink at temperature $T$. The second engine $B$ receives the heat at temperature $T$ and rejects to its sink at temperature $T_2$. For what value of $T$ the efficiencies of the two engines are equal?

A monoatomic gas is supplied heat $Q$ very slowly keeping the pressure constant. The work done by the gas will be

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

The isothermal Bulk modulus of an ideal gas at pressure $P$ 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 ?