The number of molecules in a gas at pressure $1.64 \times 10^{-3} \text{ atm}$ and temperature $200 \text{ K}$ having the volume $1 \text{ cc}$ is:

$A$ monoatomic ideal gas of two moles is taken through a cyclic process starting from $1$ as shown. Given $\frac{V_2}{V_1} = 2$ and $\frac{V_4}{V_1} = 4$. The temperature at state $1$ is $T_1 = 27\,^oC$. Find the temperature at state $2$,i.e.,$T_2$ in $K$.

The figure shows the isotherms of a fixed mass of an ideal gas at three temperatures $T_A, T_B$ and $T_C$. Then:

Find the value of the universal gas constant $R$ in $J \ mol^{-1} K^{-1}$.

Which of the following shows the correct relationship between the pressure $P$ and density $\rho$ of an ideal gas at constant temperature?

One mole of an ideal gas undergoes a process in which pressure $P$ varies with volume $V$ as $P = 3 - g \left(\frac{V}{V_0}\right)^2$, where $V_0$ and $g$ are constants. The maximum temperature attainable by the ideal gas during this process is ($All$ quantities are in $SI$ units and $R$ is the gas constant).