The efficiency of a heat engine is $\eta$ and the coefficient of performance of a refrigerator is $\beta$. Then:

In the following figure,four curves $A, B, C$ and $D$ are shown. The curves are

Two cylinders of equal size are filled with an equal amount of ideal diatomic gas at room temperature. Both cylinders are fitted with pistons. In cylinder $A$,the piston is free to move (isobaric process),while in cylinder $B$,the piston is fixed (isochoric process). When the same amount of heat is supplied to both cylinders,the temperature of the gas in cylinder $A$ rises by $30\, K$. What will be the rise in temperature of the gas in cylinder $B$ (in $;K$)?

One mole of a gas expands such that its volume $V$ changes with absolute temperature $T$ in accordance with the relation $V = K T^2$,where $K$ is a constant. If the temperature of the gas changes by $60 \text{ K}$,then the work done by the gas is ($R$ is the universal gas constant).

Air in a cylinder is suddenly compressed by a piston,which is then maintained at the same position. With the passage of time,

$A$ gas expands with temperature according to the relation,$V=k T^{2/3}$,where $k$ is a constant. Work done when the temperature changes by $60 \ K$ is ($R=$ universal gas constant.) (in $R$)