The densities of two gases are in the ratio $1:2$ and their temperatures are in the ratio $2:1$. What is the ratio of their corresponding pressures?

$A$ $3.7 \ g$ mass of a gas occupies a certain volume at $25 \ ^\circ C$. The same volume is occupied by $0.184 \ g$ of $H_2$ gas at the same pressure and $17 \ ^\circ C$. Calculate the molar mass of the gas.

Derive the relation between density $(d)$ and molar mass $(M)$ for an ideal gas.

During a reversible adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $\frac{C_p}{C_V}$ for the gas is:

The isotherms of an ideal gas at $T_1, T_2, T_3$ along with their slopes $(m)$ are shown in the graph. If $T_1 > T_2 > T_3$,then the correct order of slopes of these isotherms is:

At $240.55 \ K$,for one mole of an ideal gas,a graph of $P$ (on $y$-axis) and $V^{-1}$ (on $x$-axis) gave a straight line passing through the origin. Its slope $(m)$ is $2000 \ J \ mol^{-1}$. What is the kinetic energy (in $J \ mol^{-1}$) of the ideal gas?