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

Read the following statements:
$A.$ When the small temperature difference between a liquid and its surroundings is doubled,the rate of loss of heat of the liquid becomes twice.
$B.$ Two bodies $P$ and $Q$ having equal surface areas are maintained at temperatures $10^{\circ}C$ and $20^{\circ}C$. The thermal radiation emitted in a given time by $P$ and $Q$ are in the ratio $1:1.15$.
$C.$ $A$ Carnot engine working between $100 K$ and $400 K$ has an efficiency of $75\%$.
$D.$ When the small temperature difference between a liquid and its surroundings is quadrupled,the rate of loss of heat of the liquid becomes twice.
Choose the correct answer from the options given below:

One mole of an ideal monoatomic gas undergoes the following four reversible processes:
Step $1$: It is first compressed adiabatically from volume $8.0 \, m^{3}$ to $1.0 \, m^{3}$.
Step $2$: Then expanded isothermally at temperature $T_{1}$ to volume $10.0 \, m^{3}$.
Step $3$: Then expanded adiabatically to volume $80.0 \, m^{3}$.
Step $4$: Then compressed isothermally at temperature $T_{2}$ to volume $8.0 \, m^{3}$.
Then,$T_{1} / T_{2}$ is:

Two cylinders of equal size are filled with an equal amount of ideal diatomic gas at room temperature. Both cylinders are fitted with pistons. In cylinder $A$,the piston is free to move (isobaric process),while in cylinder $B$,the piston is fixed (isochoric process). When the same amount of heat is supplied to both cylinders,the temperature of the gas in cylinder $A$ rises by $30\, K$. What will be the rise in temperature of the gas in cylinder $B$ (in $;K$)?

If a heat engine and a refrigerator are working between the same two temperatures $T_1$ and $T_2$ $(T_1 > T_2)$,then the ratio of the efficiency of the heat engine to the coefficient of performance of the refrigerator is:

$10 \text{ mole}$ of oxygen is heated at constant volume from $30^{\circ} C$ to $40^{\circ} C$. The change in the internal energy of the gas is . . . . . . $\text{cal}$. (The molecular specific heat of oxygen at constant pressure, $C_p = 7 \text{ cal/mol}^{\circ} C$ and $R = 2 \text{ cal/mol}^{\circ} C$.)