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 $2V$?

$A$ thermodynamic process for one mole of an ideal gas is shown below on a $P-V$ diagram. If $V_{2} = 2V_{1}$, then the ratio of temperature $T_{2} / T_{1}$ 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?

Consider a $P - V$ diagram in which the path followed by one mole of perfect gas in a cylindrical container is shown in the figure.
$(a)$ Find the work done when the gas is taken from state $1$ to state $2$.
$(b)$ What is the ratio of temperature $\frac{T_1}{T_2}$ if $V_2 = 2V_1$?
$(c)$ Given the internal energy for one mole of gas at temperature $T$ is $\frac{3}{2}RT$,find the heat supplied to the gas when it is taken from state $1$ to $2$,with $V_2 = 2V_1$.

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).

$A$ gas expands in such a way that its pressure and volume satisfy the condition $PV^2 = \text{constant}$. Then the temperature of the gas