Two rigid boxes containing different ideal gases are placed on a table. Box $A$ contains one mole of nitrogen at temperature $T_0$, while box $B$ contains one mole of helium at temperature $\left( {\frac{7}{3}} \right){T_0}$. The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases, $T_f$ in terms of $T_0$ is

Which one of the following gases possesses the largest internal energy

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

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

Choose the incorrect statement from the following

$S1$: The efficiency of a heat engine can be $1$, but the coefficient of performance of a refrigerator can never be infinity

$S2$: The first law of thermodynamics is basically the principle of conservation of energy

$S3$: The second law of thermodynamics does not allow several phenomena consistent with the first law

$S4$: A process, whose sole result is the transfer of heat from a colder to a hotter object is impossible