RMS and KE Expressions

Q. A vessel is partitioned in two equal halves by a fixed diathermic seperator. Two different ideal gases are filled in the left($L$) and right($R$) halves. The rms speed of the molecules in $L$ part is equal to the mean speed in the $R$ part. Then the ratio of the mass of a molecule in $L$ part to that of a molecule in $R$ part is

1. $\frac{\sqrt{3}}{2}$
2. $\frac{\sqrt{\pi }}{2}$
3. $\frac{\sqrt{2}}{3}$
4. $\frac{3\pi }{8}$

Q. $O_2$ is $16$ times heavier than $H_2$. If at the same temperature the $O_2$ molecules have average kinetic energy $E,$ then at the same temperature the average kinetic energy of $H_2$ molecules will be

1. $\frac{E}{4}$
2. $4E$
3. $E$
4. $\frac{E}{16}$

Q.

If the rms speed of nitrogen molecules is $490m{s}^{-1}$ at 273K, find the rms speed of hydrogen molecules at the same temperature -

1. 1580 m/s

2. 1830 m/s

3. 1700 m/s

4. 2150 m/s

Q. A cylindrical container is divided in two equal parts by a diathermic piston. Different ideal gases are filled in the two parts. Find the ratio of the mass of the molecules of the gas in the lower part to that of the upper part, if the root mean square velocity of molecules in the lower part is equal to the mean velocity of molecules in the upper part.

1. $1.224$
2. $1.178$
3. $1.288$
4. $1.128$

Q. How many times a diatomic gas should be expanded adiabatically so as to reduce the root mean square velocity to half?

1. $64$
2. $32$
3. $16$
4. $8$

Q. A box contains $N$ molecules of a perfect gas at temperature $T_1$ and pressure $P_1$. The number of molecules in the box is doubled keeping the total kinetic energy of the gas same as before. If the new pressure and temperature are $P_2$ are $T_2$ respectively, then

1. $P_2=P_1,T_2=T_1$
2. $P_2=P_1,T_2=\frac{T_1}{2}$
3. $P_2=2P_1,T_2=T_1$
4. $P_2=2P_1,T_2=\frac{T_1}{2}$

Q. If pressure is assumed to be constant, at what temperature will the rms speed of gas molecules increase by $10\%$ of the rms speed at STP?

1. $57.3\text{K}$
2. $57.3{}^{\circ }\text{C}$
3. $557.3\text{K}$
4. $-57.3{}^{\circ }\text{C}$

Q. If the rms velocity of a gas is $v$, then

1. $v^{2}T=\text{constant}$
2. $v^2/T=\text{constant}$
3. $v{T}^2=\text{constant}$
4. $v$ is independent of $T$

Q.

You have been given a box filled with two gases - oxygen, and an unknown gas. It is seen that at any temperature of the mixture, the rms speed of the unknown gas is always four times that of oxygen. Can you identify this gas?

1. Hydrogen

2. Helium

3. Carbon dioxide

4. Argon

Q. A gas mixture consists of $2$ moles of $O_2$ and $4$ moles of Ar at temperature $T$. Neglecting all vibrational modes, the total internal energy of the system is

1. 15 RT
2. 9 RT
3. 11 RT
4. 15 RT

Q. A vessel is partitioned in two equal halves by a fixed diathermic seperator. Two different ideal gases are filled in the left($L$) and right($R$) halves. The rms speed of the molecules in $L$ part is equal to the mean speed in the $R$ part. Then the ratio of the mass of a molecule in $L$ part to that of a molecule in $R$ part is

1. $\frac{\sqrt{3}}{2}$
2. $\frac{\sqrt{\pi }}{2}$
3. $\frac{\sqrt{2}}{3}$
4. $\frac{3\pi }{8}$