$A$ 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:

For an ideal gas, a cyclic process $ABCA$ as shown in the $P-T$ diagram, when presented in a $P-V$ plot, would be:

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 gases have the same initial pressure,volume,and temperature. They expand to the same final volume,one adiabatically and the other isothermally.

What is an isochoric process and a cyclic process? Write the first law of thermodynamics for an ideal gas.

An ideal gas undergoes four different processes from the same initial state as shown in the figure below. Those processes are adiabatic,isothermal,isobaric and isochoric. The curve which represents the adiabatic process among $1, 2, 3$ and $4$ is