An ideal gas of molar mass $M$ is contained in a vertical tube of height $H$,closed at both ends. The tube is accelerating vertically upwards with acceleration $g$. Then,the ratio of pressure at the bottom $(P_B)$ and the midpoint $(P_m)$ of the tube will be:

This question has Statement-$1$ and Statement-$2$. Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement-$1$: The internal energy of a perfect gas is entirely kinetic and depends only on the absolute temperature of the gas and not on its pressure or volume.
Statement-$2$: $A$ perfect gas is heated keeping pressure constant and later at constant volume. For the same amount of heat,the temperature rise of the gas at constant pressure is lower than that at constant volume.

The adiabatic elasticity of hydrogen gas $(\gamma = 1.4)$ at $NTP$ is

An insulated box containing a diatomic gas of molar mass $M$ is moving with velocity $v$. The box is suddenly stopped. The resulting change in temperature is :-

Two boxes containing different ideal gases are placed on a table. Box $A$ contains $1 \text{ mole}$ of nitrogen gas at temperature $T_o$,and box $B$ contains $1 \text{ mole}$ of helium gas at temperature $(7/3) T_o$. If they are brought into thermal contact such that both gases reach a final common temperature $T_f$,what is the final temperature $T_f$ in terms of $T_o$? (Neglect the heat capacity of the boxes.)

$A$ closed vessel contains $10 \ g$ of an ideal gas $X$ at $300 \ K$,which exerts $2 \ atm$ pressure. At the same temperature,$80 \ g$ of another ideal gas $Y$ is added to it and the pressure becomes $6 \ atm$. The ratio of root mean square velocities of $X$ and $Y$ at $300 \ K$ is