Neon gas of a given mass expands isothermally to double its volume. What should be the further fractional decrease in pressure,so that the gas when adiabatically compressed from that state,reaches the original state?

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 $540 J$.

Two moles of a monoatomic ideal gas is confined in a container and is heated such that its temperature increases by $10\,^{\circ}C$. The approximate change in its internal energy is ..... $J$. $(R = 8.31\, J/mol\cdot K)$

$A$ given mass of a gas is compressed isothermally until its pressure is doubled. It is then allowed to expand adiabatically until its original volume is restored and its pressure is then found to be $0.75$ of its initial pressure. The ratio of the specific heats of the gas is approximately:

$A$ 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 (Take $\gamma = 5/3$)

Match the List-$I$ with List-$II$:

List-$I$	List-$II$
$A$. Pressure varies inversely with volume of an ideal gas.	$I$. Adiabatic process
$B$. Heat absorbed goes partly to increase internal energy and partly to do work.	$II$. Isochoric process
$C$. Heat is neither absorbed nor released by a system.	$III$. Isothermal process
$D$. No work is done on or by a gas.	$IV$. Isobaric process