Kinetic energy per unit volume is $E$. The pressure exerted by the gas is given by

If the mass of each molecule of a gas kept at a constant pressure $P$ in a container is halved and their speed is doubled,what will be the resulting pressure of the gas?

In a vessel,the gas is at pressure $P_0$. If the mass of all the molecules is halved and their speed is doubled,then the resultant pressure will be

If the number of hydrogen molecules is twice the number of oxygen molecules at the same temperature,what is the ratio of their total kinetic energies? (Hydrogen : Oxygen)

What is the kinetic energy of one gram mole of a gas at standard temperature and pressure? $(R = 8.31 \ J/mol \cdot K)$

Consider a rectangular block of wood moving with a velocity $v_{0}$ in a gas at temperature $T$ and mass density $\rho$. Assume the velocity is along the x-axis and the area of cross-section of the block perpendicular to $v_{0}$ is $A$. Show that the drag force on the block is $4\rho A v_{0} \sqrt{\frac{kT}{m}}$,where $m$ is the mass of the gas molecule.