During the melting of a slab of ice at $273 \, K$ at atmospheric pressure,

Initial pressure and volume of a gas are $P$ and $V$ respectively. First,its volume is expanded to $4V$ by an isothermal process,and then its volume is reduced to $V$ by an adiabatic process. Find its final pressure if $\gamma = \frac{3}{2}$.

$A$ Carnot cycle for a gas is represented in the pressure-volume $(P-V)$ diagram shown below. Consider the following statements:
$I.$ The area of $ABCD$ is the work done by the gas.
$II.$ The area of $ABCD$ is the total heat absorbed.
$III.$ The change in internal energy of the cycle is zero.
Which of the following is correct?

$540$ 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 .......... $cal$.

$A$ cyclic process $ABCA$ is shown in the $PT$ diagram. When presented on a $PV$ diagram,it would be:

One mole of a diatomic ideal gas undergoes a cyclic process $ABC$ as shown in the figure. The process $BC$ is adiabatic. The temperatures at $A, B$ and $C$ are $400 \ K, 800 \ K$ and $600 \ K$ respectively. Choose the correct statement.