In the $P-V$ diagram shown, the gas does $5\,J$ of work in isothermal process $ab$ and $4\,J$ in adiabatic process $bc$ .   .... $J$ will be the change in internal energy of the gas in straight path $c$ to $a$ ?

In a thermodynamic process helium gas obeys the law $TP^{-2 /5} =$ constant. The heat given to the gas when the temperature of $2$ moles of the gas is raised from $T$ to $4T$ $(R$ is the universal gas constant) is :-

A thermodynamic system is taken through the cycle $PQRSP$ process. The net work done by the system is  .... $J$

A vessel contains an ideal monoatomic gas which expands at constant pressure, when heat $Q$ is given to it. Then the work done in expansion is : 

A Carnot engine has an efficiency of $1/6$. When the temperature of the sink is reduced by $62\,^oC$, its efficiency is doubled. The temperatures of the source and the sink are, respectively

An ideal monoatomic gas is taken round the cycle $ABCDA$ as shown in following $P-V$ diagram. The work done during the cycle is