For a monoatomic gas, the work done at constant pressure is $W$. The heat supplied at constant volume for the same rise in temperature of the gas is

The initial state of a certain gas is $(P_i, V_i, T_i)$. It undergoes expansion until its volume becomes $V_f$. Consider the following two cases:
$(a)$ The expansion takes place at constant temperature.
$(b)$ The expansion takes place at constant pressure.
Plot the $P-V$ diagram for each case. In which of the two cases is the work done by the gas more?

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).

$A$ gas may expand either adiabatically or isothermally. $A$ number of $P-V$ curves are drawn for the two processes over different ranges of pressure and volume. It will be found that:

$A$ monoatomic gas of 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 (ratio of specific heats $\gamma = \frac{5}{3}$)

Match the following lists.

List-$I$	List-$II$
$A$. Zeroth law of thermodynamics	$I$. Direction of flow of heat
$B$. First law of thermodynamics	$II$. Work done is zero
$C$. Free expansion of a gas	$III$. Thermal equilibrium
$D$. Second law of thermodynamics	$IV$. Law of conservation of energy

The correct answer is: