$A$ gas expands with temperature according to the relation $V = k T^{2/3}$. What is the work done when the temperature changes by $30^{\circ}C$ (in $R$)?

The figure shows a process $AB$ undergone by $2$ moles of an ideal diatomic gas. The process $AB$ follows the relation $VT = \text{constant}$. Given $T_1 = 300 \text{ K}$ and $T_2 = 500 \text{ K}$ ($R$ is the gas constant).

$A$ perfect gas is found to obey the relation $PV^{3/2} =$ constant,during an adiabatic process. If such a gas,initially at a temperature $T$,is compressed adiabatically to half its initial volume,then its final temperature will be

An ideal gas undergoes a polytropic process given by the equation $PV^n = \text{constant}$. If the molar heat capacity of the gas during this process is the arithmetic mean of its molar heat capacity at constant pressure $(C_P)$ and constant volume $(C_V)$, then the value of $n$ is ..............

One mole of an ideal gas at temperature $T_1$ expands according to the law $\frac{P}{V^2} = a$ (constant). The work done by the gas until the temperature of the gas becomes $T_2$ is:

One mole of an ideal gas undergoes a process $PV^3 = \text{constant}$, where $P$ and $V$ are pressure and volume respectively. Let $W$ be the work done by the gas as its temperature is increased by $\Delta T$. The value of $|W|$ is ($R$ is the universal gas constant).