$540$ calories of heat converts $1$ cubic centimeter of water at $100\,^oC$ into $1671$ cubic centimeter of steam at $100\,^oC$ at a pressure of one atmosphere. Then the work done against the atmospheric pressure is nearly .......... $cal$.

Two gases $A$ and $B$ are filled at the same pressure in separate cylinders with movable pistons of radius $r_A$ and $r_B$,respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure,the pistons of gas $A$ and $B$ are displaced by $16 \ cm$ and $9 \ cm$,respectively. If the change in their internal energy is the same,then the ratio $\frac{r_A}{r_B}$ is equal to

Two moles of a gas are expanded to double their volume by two different processes. One is isobaric and the other is isothermal. If $W_1$ and $W_2$ are the works done, respectively, then:

The relation between the efficiency $\eta$ of a heat engine and the coefficient of performance $\alpha$ of a refrigerator is:

$A$ monoatomic gas at pressure $P$ having volume $V$ expands isothermally to a volume $2V$ and then adiabatically to a volume $16V$. The final pressure of the gas is $\left(\gamma = \frac{5}{3}\right)$.

An ideal gas goes through a reversible cycle $a \to b \to c \to d$ and has the $V - T$ diagram shown below. Processes $d \to a$ and $b \to c$ are adiabatic. The corresponding $P - V$ diagram for the process is (all figures are schematic and not drawn to scale):