An ideal gas undergoes a thermodynamic process described by the equation: $PV^2 = C$, where $C$ is a constant. The gas transitions from an initial state $(P_1, V_1, T_1)$ to a final state $(P_2, V_2, T_2)$. Which of the following statements is correct?

The volume ($V$) of a monatomic gas varies with its temperature ($T$), as shown in the graph. The ratio of work done by the gas to the heat absorbed by it when it undergoes a change from state $A$ to state $B$ will be:

A carnot engine having an efficiency of $\frac{1}{10}$ as a heat engine, is used as a refrigerator. If the work done on the system is $10\text{ J}$, the amount of energy absorbed from the reservoir at lower temperature is:

An engine has an efficiency of $\frac{1}{6}$. When the temperature of the sink is reduced by $62^{\circ}\text{C}$, its efficiency is doubled. The temperature of the source is:

A refrigerator works between $4^{\circ}\text{C}$ and $30^{\circ}\text{C}$. It is required to remove $600 \text{ calories}$ of heat every second to keep the temperature of the refrigerated space constant. The power required will be: (Take, $1 \text{ cal} = 4.2 \text{ Joules}$)

When $1 \text{ kg}$ of ice at $0^{\circ}\text{C}$ melts into water at $0^{\circ}\text{C}$, the resulting change in its entropy, taking the latent heat of ice to be $80 \text{ cal/g}$, is:

One mole of an ideal diatomic gas undergoes a transition from $A$ to $B$ along a path $AB$ as shown in the figure. The change in internal energy of the gas during the transition is

The coefficient of performance of a refrigerator is $5$. If the temperature inside freezer is $-20^\circ\text{C}$, the temperature of the surroundings to which it rejects heat is

A mass of diatomic gas ($\gamma=1.4$) at a pressure of $2\text{ atm}$ is compressed adiabatically so that its temperature rises from $27^\circ\text{C}$ to $927^\circ\text{C}$. The pressure of the gas in the final state is: