A gas mixture consists of $2$ moles of oxygen and $4$ moles argon at temperature $T$. Neglecting all vibrational modes, the total internal energy of the system is

In an adiabatic expansion of a gas initial and final temperatures are ${T_1}$ and ${T_2}$ respectively, then the change in internal energy of the gas is

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 :-

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 $a$ ?

A student records $\Delta Q,\Delta U$ and $\Delta W$ for a thermodynamic cycle $A \to B \to C \to A.$ Certain entries are missing. Find correct entry in following options