If $R =$ universal gas constant, the amount of heat needed to raise the temperature of $2\, mol$ of an ideal monoatomic gas from $273\, K$ to $373\, K$ when no work is done is

A heat engine has an efficiency of $\frac{1}{6}$. When the temeprature of sink is reduced by $62^{\circ} {C}$, its efficiency get doubled. The temeprature of the source is $.....^{\circ} {C}$

$P-V$ diagram of an ideal gas is as shown. Find work done by the gas in $ABCD$ process

$P-V$ diagram for two gases during adiabatic process are shown in the figure by curves $A$ and $B$ are for

The internal energy change in a system that has absorbed $2\,\, kcal$ of heat and done $500\, J$ of work is ........... $\mathrm{J}$

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