Choose the correct statement for processes $A$ and $B$ shown in the figure.

The relation between efficiency $(\eta)$ of a Carnot engine and the coefficient of performance $(\beta)$ of a refrigerator working between the same temperatures is:

An ideal gas is subjected to a cyclic process $A B C D$ as depicted in the $p-V$ diagram given below. Which of the following curves represents the equivalent cyclic process?

What are thermodynamic processes?

Two cylinders $A$ and $B$ fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 \,K$. The piston of $A$ is free to move while that of $B$ is held fixed. The same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 \,K$, what is the rise in temperature of the gas in $B$ (in $\,K$)? (Given $\gamma = 5/3$)

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 $540 J$.