One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where $V$ is the volume and $T$ is the temperature). Which of the statements below is (are) true ?

 

Two rigid boxes containing different ideal gases are placed on a table. 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). Box A contains one mole of nitrogen at temperature $T_0$, while box $B$ contains one mole of helium at temperature $\frac{7}{3}{\mathit{ }\mathit{T}}_0$. Then the final temperature of the gases, $T_{\mathit{f}}$ in terms of $T_0$ is

The work of $146 \mathrm{kJ}$ is performed in order to compress one-kilo mole of gas adiabatically and in this process the temperature of the gas increases by $7^{\circ }\mathrm{C}.$ The gas is $\left(\mathrm{R}=8.3 \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}\right) :$ 

When a system is taken from state$\mathrm{i}$ to state $\mathrm{f}$ along the path$\mathrm{iaf}$, it is found that $Q=50 \mathrm{cal}$ and $W=20 \mathrm{cal}$. Along the path$\mathrm{ibf} Q=36 \mathrm{cal}.$ $W$ along the path $\mathrm{ibf}$ is

A diatomic ideal gas is used in a Carnot engine as the working substance. If, during the adiabatic expansion part of the cycle the volume of the gas increases from $\mathrm{V}$ to $32 \mathrm{V}$, the efficiency of the engine is :