Two cylinders contain the same amount of an ideal monatomic gas. The same amount of heat is given to both cylinders. If the temperature rise in cylinder $A$ is $T_0$,then the temperature rise in cylinder $B$ will be:

$A$ graph is drawn between absolute temperature and volume of $3$ moles of helium gas as shown in the figure. If $5 \text{ cal}$ of heat is used in the process, then the work done is (in $\text{ J}$)

$A$ sample of gas expands from volume ${V_1}$ to ${V_2}$. The amount of work done by the gas is greatest when the expansion is

The temperature of $1$ mole of an ideal monoatomic gas is increased by $50^{\circ} C$ at constant pressure. The total heat added and change in internal energy are $E_1$ and $E_2$,respectively. If $\frac{E_1}{E_2}=\frac{x}{9}$,then the value of $x$ is . . . . . . .

$10 \text{ mole}$ of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from $P_1$ to $P_2$ at constant volume $V = 1 \text{ m}^3$ is $\alpha \text{ Joule}$ ($P_1 = 21.7 \text{ Pa}$, $P_2 = 30 \text{ Pa}$, $C_v = 21 \text{ J/K} \cdot \text{mol}$, $R = 8.3 \text{ J/mol} \cdot \text{K}$). The value of $\alpha$ is . . . . . . .

Which of the following graphs between pressure $(P)$ and volume $(V)$ correctly shows an isochoric process?