Mean Free Path and Real Gases PYQs: JEE Mains Physics

Showing 1–18 of 18 questions

1. 1. 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 \( 32\times10^{18}/s \) then collision frequency in gas A is__________/s. 2026 Easy
2. 2. The mean free path of a molecule of diameter \(5\times10^{-10}\) m at the temperature \(41^{\circ}C\) and pressure \(1.38\times10^{5}Pa\), is given as ___________ m.
   (Given \(k_{B}=1.38\times10^{-23}J/K\)). 2026 Medium
3. 3. The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are \(3 \times 10^{-7} \mathrm{~m}\) and \(600 \mathrm{~m} / \mathrm{s}\) respectively. Find the frequency of its collisions. 2025 Easy
4. 4. Given below are two statements : Statement \((I)\) : The mean free path of gas molecules is inversely proportional to square of molecular diameter. Statement \((II)\) : Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas. In the light of the above statements, choose the correct answer from the option given below: 2024 Hard
5. 5. If \(\mathrm{n}\) is the number density and \(\mathrm{d}\) is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by _______. 2024 Hard
6. 6. If the collision frequency of hydrogen molecules in a closed chamber at \(27^{\circ} \mathrm{C}\) is \(\mathrm{Z}\), then the collision frequency of the same system at \(127^{\circ} \mathrm{C}\) is _______. 2024 Hard
7. 7. The mean free path of molecules of a certain gas at \(STP\) is \(1500\,d\), where \(d\) is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at \(373\,K\) is approximately \(..........\,d\) 2023 Medium
8. 8. According to kinetic theory of gases, \(A\). The motion of the gas molecules freezes at \(0^{\circ} C\) \(B\). 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 temperature is increased keeping pressure constant. \(D\). Average kinetic energy per molecule per degree of freedom is \(\frac{3}{2} k_{B} T\) (for monoatomic gases) Choose the most appropriate answer from the options given below 2022 Medium
9. 9. A system consists of two types of gas molecules \(A\) and \(B\) having same number density \(2 \times\) \(10^{25}\, / {m}^{3}\). The diameter of \({A}\) and \({B}\) are \(10\, \stackrel{\circ}{{A}}\) and \(5\, \stackrel{\circ}{{A}}\) respectively. They suffer collision at room temperature. The ratio of average distance covererd by the molecule \(A\) to that of \(B\) between two successive collision is \(.....\,\times 10^{-2}\) 2021 Medium
10. 10. Calculate the value of mean free path \((\lambda)\) for oxygen molecules at temperature \(27^{\circ}\, C\) and pressure \(1.01 \times 10^{5} \,Pa\). Assume the molecular diameter \(0.3 \,nm\) and the gas is ideal. \(\left( k =1.38 \times 10^{-23}\, J\,K ^{-1}\right)\) (in \(nm\)) 2021 Hard
11. 11. An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true\(?\) \((A)\) the mean free path of the 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. 2020 Medium
12. 12. In a dilute gas at pressure \(P\) and temperature \(T\), the mean time between successive collisions of a molecule varies with \(T\) as 2020 Medium
13. 13. Two gases-argon (atomic radius \(0.07 \;\mathrm{nm}\),atomic weight \(40\) ) and xenon (atomic radius \(0.1\; \mathrm{nm},\) atomic weight \(140\) ) have the same number density and are at the same temperature. The raito of their respective mean free times is closest to 2020 Medium
14. 14. Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean collision time between the gas molecule changes from \(\tau_{1}\) to \(\tau_{2} .\) If \(\frac{C_{p}}{C_{v}}=\gamma\) for this gas then a good estimate for \(\frac{\tau_{2}}{\tau_{1}}\) is given by : 2020 Hard
15. 15. An ideal gas is enclosed in a cylinder at pressure of \(2\,atm\) and temperature, \(300\,K.\) The mean time between two successive collisions is \(6 \times 10^{-8}\, s.\) If the pressure is doubled and temperature is increased to \(500\,K,\) the mean time between two successive collisions will be close to 2019 Hard
16. 16. An ideal gas has molecules with \(5\,\) degrees of freedom. The ratio of specific heats at constant pressure \((C_p)\) and at constant volume \((C_v)\) is 2017 Easy
17. 17. Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as \(V ^q\), where \(V\) is the volume of the gas. The value of \(q\) is \(\left( {\gamma = \frac{{{C_P}}}{{{C_V}}}} \right)\) 2015 Hard
18. 18. Modern vacuum pumps can evacuate a vessel down to a pressure of \(4.0 \times {10^{ - 15}}\, atm\) at room temperature \((300\, K)\). Taking \(R = 8.0\, JK^{-1}\, mole^{-1}\) , \(1\, atm = 10^5\, Pa\) and \(N_ {Avogadro} = 6 \times 10^{23}\, mole^{-1}\) , the mean distance between molecules of gas in an evacuated vessel will be of the order of 2014 Medium

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