RMS and KE Expressions

Q. At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at – 20 °C ? (atomic mass of Ar = 39.9 u, of He = 4.0 u).

Q. Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains neon (monatomic), the second contains chlorine (diatomic), and the third contains uranium hexafluoride (polyatomic). Do the vessels contain equal number of respective molecules ? Is the root mean square speed of molecules the same in the three cases? If not, in which case is v_rms the largest ?

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. 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.

Our universe has been continuously expanding since its formation at the Big Bang, thus gradually reducing the density of its major constituents - hydrogen and helium, and the average temperature to 2.7K (associated with the so-called microwave background radiation left over from the Big Bang). What is the rms speed of hydrogen molecules at this temperature?

1. 183 m/s

2. 125 m/s

3. 240 m/s

4. 314 m/s

Q. A famous relation in physics relates 'moving mass' m to the 'rest mass' $m_0$ of a particle in terms of its speed v and the speed of light, c. (This relation first arose asa consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant c. He writes :
$m=\frac{m_o}{{(1-v^2)}^{1/2}}$
Guess where to put the missing c.

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. Two closed vessels A, B are at same temperature T and contain gases which obey maxwellian distribution of velocities. Vessel A contains O2, and B contain mixture of H2 and O2. If the average speed of the O2 molecule in vessel A is v1, then average speed of H2 in container B is

Q.

Under constant pressure, the temperature of 3 mol of an ideal monoatomic gas is raised by 15 K. What is the change in average kinetic energy per atom?

1. 1.021 eV

2. 0.00194 eV

3. 0.2171 eV

4. 0.0352 eV

Q.

You have but one molecule of Hydrogen $\left(H_2\right),$ meandearing about in the vast emptiness of a $1c{m}^3$ closed box, at a speed of 500 m/s, bouncing off from one wall to the next. What are the rms speed and the temperature inside the box?

1. 500 m/s; temperature cannot be determined

2. 512 m/s; 20k

3. 250000 m/s; 20 k

4. 500 m/s; 20 k

Q.

At what temperature does the rms speed of oxygen molecules equal the escape velocity of - (i) Earth, (ii) the Moon? The gravitational acceleration of the Moon is 0.6g.

1. 

2. 

3. 

4. 

Q.

At what temperature does the rms speed of oxygen molecules equal the escape velocity of - (i) Earth, (ii) the Moon? Assume gravitational acceleration at the moon is 0.6g.

1. $5.6\times {10}^{5}K;7.0\times {10}^{5}K$

2. $2.4\times {10}^{6}K;7.0\times {10}^{3}K$

3. $3.5\times {10}^{4}K;700K$

4. $1.6\times {10}^{5}K;7.0\times {10}^{3}K$

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. 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.

Calculate the rms speed of nitrogen at STP (pressure = 1 atm and temperature = $0^{\circ }C$). The density of nitrogen in these conditions is $1.25kg{m}^{-3}$.

1. 490 m/s

2. 510 m/s

3. 410 m/s

4. 370 m/s

Q. Two closed vessels A, B are at same temperature T and contain gases which obey maxwellian distribution of velocities. Vessel A contains O2, and B contain mixture of H2 and O2. If the average speed of the O2 molecule in vessel A is v1, then average speed of H2 in container B is

Q.

What is the translational kinetic energy of a Helium molecule (He) at 1500 K?

1. 2.189 eV

2. 0.194 eV

3. 1.215 eV

4. 10.068 eV

Q.

You have but one molecule of Hydrogen $\left(H_2\right),$ meandering about in the vast emptiness of a $1c{m}^3$ closed box, at a speed of 500 m/s, bouncing off from one wall to the next. What are the rms speed and the temperature inside the box?

1. 512 m/s; 20k
2. 250000 m/s; 20 k
3. 500 m/s; 20 k
4. 500 m/s; temperature cannot be determined