At $27\,^{\circ}C$ and $1\,atm$ pressure,the density of a gas is $d$. At what temperature will its density become $0.75d$ if the pressure is kept constant?

An open vessel at $27\,^oC$ is heated such that $\frac{3}{5}$ of the air in it is expelled. Assuming the volume of the vessel remains constant,calculate the temperature in $K$ to which the vessel was heated.

How many times the volume of a diatomic gas should be increased reversibly and adiabatically in order to reduce its $RMS$ velocity to half of its initial value?

If $N_2$ gas is compressed at $2 \text{ atm}$ from $9.0 \text{ L}$ to $3.0 \text{ L}$ at $300 \text{ K}$, find the final pressure at the same temperature. (in $\text{ atm}$)

In the gas equation $PV = nRT$,the universal gas constant $R$ depends on:

The gas equation $PV = nRT$ is applicable for which of the following conditions?