During an experiment, an ideal gas is found to obey an additional law $VP^2 = \text{constant}$. The gas is initially at temperature $T$ and volume $V$. What will be the temperature of the gas when it expands to a volume $2V$?

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 ..............

$0.02 \, mol$ of an ideal diatomic gas with initial temperature $20^{\circ} C$ is compressed from $1500 \, cm^3$ to $500 \, cm^3$. The thermodynamic process is such that $p V^2 = \beta$,where $\beta$ is a constant. Then,the value of $\beta$ is close to (the gas constant,$R = 8.31 \, J / K / mol$).

$A$ monoatomic gas is taken through a process $TP^{-1/3} = \text{constant}$. If heat is given to the gas, what happens to its temperature?

$2$ moles of a monoatomic gas are expanded to double its initial volume, through a process $P/V = \text{constant}$. If its initial temperature is $300\, K$, then which of the following is not true?

$1 \, \text{mole}$ of a gas expands with temperature as $V = KT^{2/3}$. What is the work done when temperature changes by $30^oC$ (in $R$)?