An ideal gas at pressure ' P ' and temperature ' T ' is enclosed in a vessel of volume ' $V$ '. Some gas leaks through a hole from the vessel and the pressure of the enclosed gas falls to ' P '. Assuming that the temperature ture of the gas remains constant during the leakage , the number of moles of the gas that have leaked is

If r.m.s. velocity of hydrogen molecules is 4 times that of an oxygen molecule at $47^{\circ} \mathrm{C}$, the temperature of hydrogen molecules is (Molecular weight of Hydrogen and Oxygen are 2 and 32 respectively)

A monoatomic ideal gas is heated at constant pressure. The percentage of total heat used in increasing the internal energy and that used for doing external work is $A$ and $B$ respectively. Then the ratio, $\mathrm{A}: \mathrm{B}$ is