## Kinetic Theory Questions and Answers Part-14

1. At a given temperature the r.m.s. velocity of molecules of the gas is
a) Same
b) Proportional to molecular weight
c) Inversely proportional to molecular weight
d) Inversely proportional to square root of molecular weight

Explanation: At a given temperature the r.m.s. velocity of molecules of the gas is inversely proportional to square root of molecular weight

2. By what factor the r.m.s. velocity will change, if the temperature is raised from 27°C to 327°C
a) $\sqrt{2}$
b) 2
c) $2\sqrt{2}$
d) 1

Explanation: 3. The speeds of 5 molecules of a gas (in arbitrary units) are as follows : 2, 3, 4, 5, 6. The root mean square speed for these molecules is
a) 2.91
b) 3.52
c) 4.00
d) 4.24

Explanation: 4. At a given temperature the ratio of r.m.s. velocities of hydrogen molecule and helium atom will be
a) $\sqrt{2} : 1$
b) $1: \sqrt{2}$
c) 1 : 2
d) 2 : 1

Explanation: $\sqrt{2} : 1$

5. If the oxygen $\left(O_{2}\right)$ has root mean square velocity of C $ms^{-1}$, then root mean square velocity of the hydrogen $\left(H_{2}\right)$ will be
a) C $ms^{-1}$
b) $\frac{1}{C} ms^{-1}$
c) 4C $ms^{-1}$
d) $\frac{C}{4} ms^{-1}$

Explanation: 4C $ms^{-1}$

6. To what temperature should the hydrogen at room temperature (27°C) be heated at constant pressure so that the R.M.S. velocity of its molecules becomes double of its previous value
a) $1200^{\circ} C$
b) $927^{\circ} C$
c) $600^{\circ} C$
d) $108^{\circ} C$

Explanation: 7. The temperature of an ideal gas is reduced from $927^{\circ} C$  to $27^{\circ} C$  . The r.m.s. velocity of the molecules becomes
a) Double the initial value
b) Half of the initial value
c) Four times the initial value
d) Ten times the initial value

Explanation: The temperature of an ideal gas is reduced from $927^{\circ} C$  to $27^{\circ} C$  . The r.m.s. velocity of the molecules becomes half of the initial value

8. The r.m.s. speed of the molecules of a gas in a vessel is $400 ms^{-1}$ . If half of the gas leaks out, at constant temperature, the r.m.s. speed of the remaining molecules will be
a) $800 ms^{-1}$
b) $400 \sqrt{2}ms^{-1}$
c) $400 ms^{-1}$
d) $200 ms^{-1}$

Explanation: $400 ms^{-1}$

9. Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will
a) Increase
b) Decrease
c) Remain same
d) Decrease for some, while increase for others

a) $1930 \sqrt{3}m/s$
d) $\frac{1930}{\sqrt{3}}ms^{-1}$ 