Five moles of an ideal gas has pressure $p_0$,volume $V_0$,and temperature $T_0$. The gas is expanded to volume $3V_0$ along a path such that the pressure $p$ changes as a function of volume $V$ as $p = p_0(V/V_0)$. The pressure is then reduced to $p_0$ while maintaining constant volume. Finally,the gas undergoes an isobaric compression until the volume and temperature return to $V_0$ and $T_0$,respectively. The total work done by the gas during the entire process is:

If ${C_V} = 4.96 \text{ cal/mole K}$,then the increase in internal energy when the temperature of $2 \text{ moles}$ of this gas is increased from $340 \text{ K}$ to $342 \text{ K}$ is ....... $\text{cal}$.

If $dQ$,$dU$,and $dW$ are heat energy absorbed,change in internal energy,and external work done respectively by a diatomic gas at constant pressure,then the ratio $dW: dU: dQ$ is:

The efficiency of a Carnot engine operating with a hot reservoir kept at a temperature of $1000 K$ is $0.4$. It extracts $150 J$ of heat per cycle from the hot reservoir. The work extracted from this engine is being fully used to run a heat pump which has a coefficient of performance $10$. The hot reservoir of the heat pump is at a temperature of $300 K$. Which of the following statements is/are correct:
$(A)$ Work extracted from the Carnot engine in one cycle is $60 J$.
$(B)$ Temperature of the cold reservoir of the Carnot engine is $600 K$.
$(C)$ Temperature of the cold reservoir of the heat pump is $270 K$.
$(D)$ Heat supplied to the hot reservoir of the heat pump in one cycle is $540 J$.

$N$ moles of an ideal diatomic gas are in a cylinder at temperature $T$. Suppose on supplying heat to the gas, its temperature remains constant but $n$ moles get dissociated into atoms. Heat supplied to the gas is

Two containers $A$ and $B$ contain equal volumes of an identical gas at the same pressure and temperature. The gas in container $A$ is compressed to half its original volume isothermally,while the gas in container $B$ is compressed to half its original volume adiabatically. The ratio of the final pressure of gas in container $B$ to that of gas in container $A$ is