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 :-

$3\, moles$ of an ideal monoatomic gas perform a cycle as shown in the figure. The gas temperature in different states are: $T_1 = 400\, K$, $T_2 = 800\, K$, $T_3 = 2400\, K$ and $T_4 = 1200\,K$. The work done by the gas during the cycle is …… $kJ$

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

An ideal monoatomic gas is taken round the cycle $ABCDA$ shown in the $PV$ diagram in the given fig. The work done during the cycle is

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