Suppose an ideal gas follows the process $VP^3 = \text{constant}$. The initial temperature and volume of the gas are $T$ and $V$ respectively. If the gas expands to $27V$, then its final temperature will be:

An ideal gas follows a process described by $p V^2 = C$ from $(p_1, V_1, T_1)$ to $(p_2, V_2, T_2)$,where $C$ is a constant. Then,

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

An ideal gas is found to obey $Pv^{\frac{3}{2}} = \text{constant}$ during an adiabatic process. If such a gas initially at a temperature $T$ is adiabatically compressed to $\frac{1}{4}$th of its volume,then its final temperature is

During an experiment, an ideal gas is found to obey a condition $VP^2 = \text{constant}$. The gas is initially at a temperature $T$, pressure $P$, and volume $V$. The gas expands to volume $4V$. Which of the following statements is correct?

$A$ 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 $R$)?