If $P, V, M, T,$ and $R$ represent pressure,volume,molar mass,temperature,and gas constant respectively,then the density of an ideal gas is given by:

What will be the value of the gas constant $R$ when pressure is expressed in $dyne \, m^{-2}$ and volume in $mm^3$?

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?

The density of ammonia gas at $27^{\circ}C$ and $3 \, atm$ pressure is approximately:

$A$ hot air balloon has a volume of $2000 \text{ dm}^3$ at $99^\circ\text{C}$. What is the new volume if the air in the balloon cools to $80^\circ\text{C}$ (in $\text{ dm}^3$)?

$A$ container is divided into two equal parts $A$ and $B$ containing $H_2$ and $O_2$ respectively,each at $1 \ atm$ pressure. If the wall separating the two sections is removed,what happens to the pressure?