Q. No.An ideal gas is confined in a closed container and slowly heated. As the temperature rises, which of the following statements are correct?
| (A) | The mean free path of gas molecules decreases. |
| (B) | The mean collision time between the molecules decreases. |
| (C) | The mean free path remains unchanged. |
| (D) | The mean collision time remains unchanged. |
Choose the correct option from the given ones:
| 1. | (C) and (D) only |
| 2. | (A) and (B) only |
| 3. | (A) and (D) only |
| 4. | (B) and (C) only |
Subtopic: Â Mean Free Path |
Level 3: 35%-60%
Please attempt this question first.
Hints
Please attempt this question first.
If the ratio of the number density per cm3 of the two gases is \(5:3\) and the ratio of the diameters of the molecules of the two gases is \(4:5,\) then, the ratio of the mean free path of molecules of two gases is:
| 1. | \(\dfrac{16}{15}\) | 2. | \(\dfrac{15}{16}\) |
| 3. | \(\dfrac{3}{4}\) | 4. | \(\dfrac{4}{3}\) |
Subtopic: Â Mean Free Path |
 75%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
According to the kinetic theory of gases,
Choose the most appropriate answer from the options given below:
| (A) | the motion of the gas molecules freezes at \(0^\circ\text C.\) |
| (B) | the mean free path of gas molecules decreases if the density of molecules is increased. |
| (C) | the mean free path of gas molecules increases if the temperature is increased keeping the pressure constant. |
| (D) | average kinetic energy per molecule per degree of freedom is \(\dfrac32k_B T\) (for monoatomic gases). |
| 1. | (A) and (C) only |
| 2. | (B) and (C) only |
| 3. | (A) and (B) only |
| 4. | (C) and (D) only |
Subtopic: Â Mean Free Path |
 60%
Level 2: 60%+
Hints
An ideal gas is enclosed in a cylinder at pressure of \(2~\text{atm}\) and temperature \(300 ~\text{K.}\) The mean time between two successive collisions is \(6\times 10^{-8}~\text{s}.\) If the pressure is doubled and temperature is increased to \(500 ~\text{K,}\) the mean time between two successive collisions will be close to:
1. \(2\times 10^{-7}~\text{s}\)
2. \(4\times 10^{-8}~\text{s}\)
3. \(0.5\times 10^{-8}~\text{s}\)
4. \(3\times 10^{-6}~\text{s}\)
1. \(2\times 10^{-7}~\text{s}\)
2. \(4\times 10^{-8}~\text{s}\)
3. \(0.5\times 10^{-8}~\text{s}\)
4. \(3\times 10^{-6}~\text{s}\)
Subtopic: Â Mean Free Path |
 69%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
The plot that depicts the behaviour of the mean free time \(\tau\) (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature \(( T ),\) qualitatively, is:
(Graphs are schematic and not drawn to scale)
(Graphs are schematic and not drawn to scale)
| 1. |  |
3. |  |
| 2. |  |
4. |  |
Subtopic: Â Mean Free Path |
 60%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
Calculate the value of the mean free path \((\lambda)\) for oxygen molecules at temperature \(27^\circ\text{C}\) and pressure \(1.01\times 10^5~\text{Pa}.\)Assume the molecular diameter \(0.3~\text{nm}\) and the gas is ideal.
\(\left({k}=1.38 \times 10^{-23}~\text{JK}^{-1}\right) \)
1. \(58~\text{nm}\)
2. \(86~\text{nm}\)
3. \(32~\text{nm}\)
4. \(102~\text{nm}\)
\(\left({k}=1.38 \times 10^{-23}~\text{JK}^{-1}\right) \)
1. \(58~\text{nm}\)
2. \(86~\text{nm}\)
3. \(32~\text{nm}\)
4. \(102~\text{nm}\)
Subtopic: Â Mean Free Path |
 67%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
A system consists of two types of gas molecules \({A}\) and \({B}\) having the same number density \({2\times10^{25}~\text{m}^3}.\) The diameter of \({A}\) and \({B}\) are \({10\mathring{A}}\) and \({5\mathring{A}}\) respectively. They suffer a collision at room temperature. The ratio of the average distance covered by molecule \({A}\) to that of \({B}\) between two successive collisions is:
1. \(15\times10^{-2}\)
2. \(10\times10^{-2}\)
3. \(20\times10^{-2}\)
4. \(25\times10^{-2}\)
1. \(15\times10^{-2}\)
2. \(10\times10^{-2}\)
3. \(20\times10^{-2}\)
4. \(25\times10^{-2}\)
Subtopic: Â Mean Free Path |
 54%
Level 3: 35%-60%
Please attempt this question first.
Hints
Please attempt this question first.
In a closed rigid chamber, the collision frequency of molecules of an ideal gas at \(27^\circ \text{C}\) is \(\nu.\) What will be the collision frequency when the gas temperature is increased to \(127^\circ \text{C}\)?
| 1. | \(\dfrac{\sqrt{3}}{2} \nu\) | 2. | \(\sqrt{\dfrac{127}{27}} \nu\) |
| 3. | \(\dfrac{2}{\sqrt{3}} \nu\) | 4. | \(\dfrac{27}{127} \nu\) |
Subtopic: Â Mean Free Path |
 59%
Level 3: 35%-60%
Please attempt this question first.
Hints
Please attempt this question first.
Consider two boxes containing ideal gases \(A\) and \(B\) such that their temperatures, pressures and number densities are same. The molecular size of \(A\) is half of that of \(B\) and mass of molecule \(A\) is four times that of \(B\). If the collision frequency in gas \(B\) is \(32\times10^{18}~\text{/s}\) then collision frequency in gas \(A\) is:
1. \(32\times10^{8}\) /s
2. \(4\times10^{8}\) /s
3. \(2\times10^{8}\) /s
4. \(8\times10^{8}\) /s
1. \(32\times10^{8}\) /s
2. \(4\times10^{8}\) /s
3. \(2\times10^{8}\) /s
4. \(8\times10^{8}\) /s
Subtopic: Â Mean Free Path |
 60%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
The mean free path of a molecule of diameter \(5 \times 10^{-10}\) at the temperature \(41^{\circ}\text{C}\) and pressure \(1.38 \times 10^5~\text{Pa}\), is given as: (in m)
(Given \(K_a= 1.38 \times 10^{-23} ~\text{J/K})\)
1. \(2 \sqrt 2 \times 10^{-10}\)
2. \(10 \sqrt 2 \times 10^{-8}\)
3. \(2 \sqrt 2 \times 10^{-8}\)
4. \( 2 \times 10^{-8}\)
(Given \(K_a= 1.38 \times 10^{-23} ~\text{J/K})\)
1. \(2 \sqrt 2 \times 10^{-10}\)
2. \(10 \sqrt 2 \times 10^{-8}\)
3. \(2 \sqrt 2 \times 10^{-8}\)
4. \( 2 \times 10^{-8}\)
Subtopic: Â Mean Free Path |
 71%
Level 2: 60%+
Please attempt this question first.
Hints
Please attempt this question first.
© 2026 GoodEd Technologies Pvt. Ltd.