$A$ gas has temperature $T$ and volume $V$. At constant pressure,if the temperature is increased by $\Delta T$,the volume increases by $\Delta V$. How does $\delta = \frac{\Delta V}{V\Delta T}$ vary with temperature?

The mass of a hydrogen atom is $3.32 \times 10^{-27} \, kg$. If $10^{23}$ atoms per second strike a wall of area $2 \, cm^2$ at an angle of $45^{\circ}$ with the normal to the wall and reflect elastically with a speed of $10^3 \, m/s$,the pressure exerted on the wall will be: $(N/m^2)$

If $v_1$ is the speed of sound in a diatomic gas at $273^{\circ}C$ and $v_2$ is the r.m.s. speed of its molecules at $273 \ K$,then $\frac{v_1}{v_2}=$

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.

$A$ 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

As per the kinetic theory of gases, which of the following statements is/are true?
$(a)$ Temperature of a gas is a measure of the average kinetic energy of a molecule.
$(b)$ Temperature of a gas depends on the nature of the gas.
$(c)$ Heavier molecules have lower average speed.
$(d)$ Lighter molecules have lower average speed.