Root Mean Square Velocity

Q. The mass of molecule $A$ is twice that of molecule $B$. The root mean square velocity of molecule $A$ is twice that of molecule $B$. If two containers of equal volume have same number of molecules, the ratio of pressure $\frac{P_A}{P_B}$ will be:

1. 8 : 1
2. 1 : 8
3. 4 : 1
4. 1 : 4

Q. The root mean square velocity of one mole of a monoatomic gas having molar mass $M$ is $u_{\text{rms}}$. The relation between the average kinetic energy $\left(E\right)$ of the gas and $u_{\text{rms}}$ is:

1. $u_{\text{rms}}=\sqrt{\frac{3E}{2M}}$
2. $u_{\text{rms}}=\sqrt{\frac{2E}{3M}}$
3. $u_{\text{rms}}=\sqrt{\frac{2E}{M}}$
4. $u_{\text{rms}}=\sqrt{\frac{E}{3M}}$

Q. Distribution of fraction of molecules with velocity is represented in the figure.

Velocity corresponding to point $X$ is:

1. $\frac{\sqrt{3}RT}{M}$
2. $\frac{\sqrt{8}RT}{M}$
3. $\frac{\sqrt{2}RT}{M}$
4. None

Q. At what temperature is the rms speed of hydrogen molecules the same as that of oxygen molecules at ${1327}^{\circ }C$ ?

1. $173K$
2. $100K$
3. $400K$
4. $523K$

Q. A gas consists of $5$ molecules with a velocity of $5{\text{m s}}^{-1}$, $10$ molecules with a velocity of $3{\text{m s}}^{-1}$ and $6$ molecules with a velocity of $6{\text{m s}}^{-1}$. The ratio of average velocity and rms velocity of the molecules is $9.5\times {10}^{-x}$. Value of $x$ is:

Q. The root mean square velocity of a monoatomic gas (molar mass $=m{\text{kg mol}}^{-1}$) is $u$. Its kinetic energy per mole $\left(E\right)$ is related to $u$ by equation:

1. $u=\sqrt{\frac{3E}{m}}$
2. $u=\sqrt{\frac{2E}{3m}}$
3. $u=\sqrt{\frac{2E}{m}}$
4. $u=\sqrt{\frac{E}{3m}}$

Q. The root mean square velocity of hydrogen is $\sqrt{5}$ times than that of nitrogen. If $T$ is the temperature of the gas, then:

1. $T_{H_2}=T_{N_2}$
2. $T_{H_2}>T_{N_2}$
3. $T_{H_2}<T_{N_2}$
4. $T_{H_2}=\sqrt{7}{T}_{N_2}$

Q. A vessel of capactity $1d{m}^3$ contains $1.03\times {10}^{23}{H}_2$ molecules exerting a pressure of $101.325\text{kPa}$. Calculate RMS speed and average speed.

1. $\begin{array}{cc}\text{RMS speed}& \text{Average speed}\\ 942.5{\text{m s}}^{-1}& 868.35{\text{m s}}^{-1}\end{array}$
2. $\begin{array}{cc}\text{RMS speed}& \text{Average speed}\\ 942.5{\text{m s}}^{-1}& 722.12{\text{m s}}^{-1}\end{array}$
3. $\begin{array}{cc}\text{RMS speed}& \text{Average speed}\\ 868.36{\text{m s}}^{-1}& 942.5{\text{m s}}^{-1}\end{array}$
4. $\begin{array}{cc}\text{RMS speed}& \text{Average speed}\\ 942.5{\text{m s}}^{-1}& 622.53{\text{m s}}^{-1}\end{array}$

Q. The root mean square velocity of hydrogen is $\sqrt{5}$ times than that of nitrogen. If $T$ is the temperature of the gas, then:

1. $T_{H_2}=T_{N_2}$
2. $T_{H_2}>T_{N_2}$
3. $T_{H_2}<T_{N_2}$
4. $T_{H_2}=\sqrt{7}{T}_{N_2}$

Q. The root mean square velocity of one mole of a monoatomic gas having molar mass $M$ is $u_{\text{rms}}$. The relation between the average kinetic energy $\left(E\right)$ of the gas and $u_{\text{rms}}$ is:

1. $u_{\text{rms}}=\sqrt{\frac{3E}{2M}}$
2. $u_{\text{rms}}=\sqrt{\frac{2E}{M}}$
3. $u_{\text{rms}}=\sqrt{\frac{2E}{3M}}$
4. $u_{\text{rms}}=\sqrt{\frac{E}{3M}}$

Q. Let, the average molar mass of air is $24.9g$. An open vessel at $27{}^{o}C$ is heated upto $t{}^{o}C$ until $1/3^{rd}$ of the air measured at final temperature excapes out. The rms velocity of air molecules at $t{}^{o}C$ is: (Take $R=8.3J{K}^{-1}mo{l}^{-1}$)

1. $340.12mse{c}^{-1}$
2. $420.35mse{c}^{-1}$
3. $632.45mse{c}^{-1}$
4. $515.25mse{c}^{-1}$

Q. At what temperature is the rms speed of hydrogen molecules the same as that of oxygen molecules at ${1327}^{\circ }C$ ?

1. $173K$
2. $100K$
3. $400K$
4. $523K$

Q. Distribution of fraction of molecules with velocity is represented in the figure.

Velocity corresponding to point $X$ is:

1. $\frac{\sqrt{2}RT}{M}$
2. $\frac{\sqrt{3}RT}{M}$
3. $\frac{\sqrt{8}RT}{M}$
4. None

Q. The ratio of the root mean square speed of $H_2$ gas at $50\text{K}$ and that of $O_2$ gas at $800\text{K}$ is:

1. 4
2. 2
3. 1
4. 0.25

Q. The molar mass of a certain gas $B$ is double than that of $A$. Also the RMS velocity of gas $A$ is $200{\text{ms}}^{-1}$ at a certain temperature. RMS velocity of gas $B$ at the temperature half of the temperature of $A$ is:

1. $200{\text{ms}}^{-1}$
2. $300{\text{ms}}^{-1}$
3. $400{\text{ms}}^{-1}$
4. $100{\text{ms}}^{-1}$

Q. Two containers are maintained at the same temperature. The first one has a volume of 8 litres and stores hydrogen at 2 atm. The other one has a volume of 4 litres and stores oxygen at 1 atm. What is the ratio of the root mean square velocities of hydrogen and oxygen?

1. 4:1
2. 1:4
3. 1:16
4. 16:1

Q. A gas consists of $5$ molecules with a velocity of $5{\text{m s}}^{-1}$, $10$ molecules with a velocity of $3{\text{m s}}^{-1}$ and $6$ molecules with a velocity of $6{\text{m s}}^{-1}$. The ratio of average velocity and rms velocity of the molecules is $9.5\times {10}^{-x}$. Value of $x$ is:

Q.

The R.M.S. velocity of hydrogen is $\sqrt{7}$ times the R.M.S. velocity of Nitrogen. If T is the temperature of the Gas, then

1. $T_{H_2}=T_{N_2}$

2. $T_{H_2}>T_{N_2}$

3. $T_{H_2}<T_{N_2}$

4. $T_{H_2}=\sqrt{7}\times T_{N_2}$

Q. Temperature at which the rms speed of $O_2$ is equal to that of neon at $300\text{K}$ is:

1. $280\text{K}$
2. $480\text{K}$
3. $680\text{K}$
4. $180\text{K}$

Q. At same temperature, calculate the ratio of average velocities of $S{O}_2$ and $C{H}_4$:

1. 2 : 3
2. 3 : 4
3. 1 : 2
4. 1 : 6

Q. The density of a gas filled in an electric lamp is $0.75\text{kg}/{\text{m}}^3$ . After the lamp has been switched on, the pressure in it increases from $4\times {10}^4\text{Pa}$ to $9\times {10}^4\text{Pa}$. What is the increase in $U_{RMS}$ ?

1. 100 m/s
2. 200 m/s
3. 300 m/s
4. None of these

Q. A vessel of capactity $1d{m}^3$ contains $1.03\times {10}^{23}{H}_2$ molecules exerting a pressure of $101.325\text{kPa}$. Calculate RMS speed and average speed.

1. $\begin{array}{cc}\text{RMS speed}& \text{Average speed}\\ 942.5{\text{m s}}^{-1}& 868.35{\text{m s}}^{-1}\end{array}$
2. $\begin{array}{cc}\text{RMS speed}& \text{Average speed}\\ 942.5{\text{m s}}^{-1}& 722.12{\text{m s}}^{-1}\end{array}$
3. $\begin{array}{cc}\text{RMS speed}& \text{Average speed}\\ 868.36{\text{m s}}^{-1}& 942.5{\text{m s}}^{-1}\end{array}$
4. $\begin{array}{cc}\text{RMS speed}& \text{Average speed}\\ 942.5{\text{m s}}^{-1}& 622.53{\text{m s}}^{-1}\end{array}$

Q. At what temperature is the rms speed of hydrogen molecules the same as that of oxygen molecules at ${1327}^{\circ }C$ ?

1. $173K$
2. $100K$
3. $400K$
4. $523K$

Q.

For a fixed amount of given gas at temperature and pressure,

1. RMS velocity > most probable velocity

2. most probable velocity < average velocity

3. RMS velocity > Average velocity

4. All of the above

Q. A gas consists of $5$ molecules with a velocity of $5{\text{m s}}^{-1}$, $10$ molecules with a velocity of $3{\text{m s}}^{-1}$ and $6$ molecules with a velocity of $6{\text{m s}}^{-1}$. The ratio of average velocity and rms velocity of the molecules is $9.5\times {10}^{-x}$. Value of $x$ is: