Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NEETPhysicsKinetic Theory of Gases

An ideal gas has an initial mean free path . If the absolute temperature of the gas is doubled and its pressure is halved, what will be the new mean free path of the gas molecules?

Options

  1. A2
  2. B4
  3. C4

Correct answer

3

Step-by-step solution

The mean free path of a gas molecule is given by: = 1 2 d^2 n From the ideal gas equation, P = nkT n = P kT Substituting n into the mean free path formula gives: = kT 2 d^2 P This shows that for a given gas, the mean free path is directly proportional to the absolute temperature and inversely proportional to the pressure: T P When the temperature is doubled ( T' = 2T ) and the pressure is halved ( P' = P 2 ), the new mean free path ' becomes: ' 2T P 2 = 4 ( T P ) Therefore, the new mean free path is 4 . Answer: 4

Practice Kinetic Theory of Gases on Quantrex Academy →

More from Kinetic Theory of Gases

Pressure exerted by an ideal gas on the walls of the container is equal to a) mean kinetic energy per unit volume. b) half of mean kinetic energy per unit volume. c) one-third of m 2026Two litre of an ideal gas at 42^ C is heated at a constant pressure to 357^ C . Then the final volume is 2026The temperature at which the mean kinetic energy of the molecules of gas is ( 1 4 )^ th of the mean kinetic energy of its molecules at 147^ C is 2026There are two vessels A and B with rigid walls containing ideal gases. The pressure, temperature and volume are P_A , T_A and V in the vessel A and P_B , T_B and V in vessel B. The 2026The pressure P , volume V and temperature T of a gas in the jar A and the other gas in the jar B is at pressure 2P , volume V/4 and temperature 2T , then the ratio of the number of 2026The temperature at which the root-mean-square speed of carbon dioxide molecules becomes just sufficient for escaping Earth's atmosphere is approximately (Mass of carbon dioxide mol 2026If the ratio of specific heat of gas = C_p C_v , then the value of C_p in terms of and gas constant R is 2026The internal energy per molecule for a diatomic (non-rigid) gas is (where k_B is Boltzmann's constant and T is absolute temperature). 2026 Full Kinetic Theory of Gases list All NEET PYQs