An ideal gas is trapped inside a test tube of cross-sectional area $20 \times 10^{-6} \,\,m^2$ as shown in the figure. The gas occupies a height $L_1$ at the bottom of the tube and is separated from air at atmospheric pressure by a mercury column of mass $0.002\,\, kg$. If the tube is quickly turned isothermally, upside down so that $L_2$ mercury column encloses the gas from below. The gas now occupies height $L_1$ in the tube. The ratio $L_1$ is [Take atmospheric pressure $= 10^5 Nm^{-2}]$ 

The following graphs shows two isotherms for a fixed mass of an ideal gas. The ratio of $r.m.s.$ speed of the molecules at temperatures $T_1$ and $T_2$ is

The ratio of de-Broglie wavelength of molecules of hydrogen and helium in two jars kept separately at temperatures of $27\,^oC$ and $127\,^oC$ respectively is

Two identical glass bulbs are interconnected by a thin glass tube at $0^o\ C$. A gas is filled in these bulb is placed in ice and another bulb is placed in hot bath, then the pressure of the gas becomes $1.5\  times$. The temperature of hot bath will be …… $^oC$

The graph which represents the variation of mean kinetic energy of molecules with temperature $t^o\ C $ is