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 $= 10^5 Nm^{-2}]$ 

$CO_2(O-C-O)$ is a triatomic gas. Mean kinetic energy of one gram gas will be (If $N-$ Avogadro's number, $k-$ Boltzmann's constant and molecular weight of $CO_2 = 44$ )

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

The gas equation $\frac{{PV}}{T} = $constant, is true for a constant mass of an ideal gas undergoing

Figure shows two flasks connected to each other. The volume of the flask $1$ is twice that of flask $2$. The system is filled with an ideal gas at temperature $100\,K$ and $200\,K$ respectively. If the mass of the gas in $1$ be $m$ then what is the mass of the gas in flask $2$