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
- A2
- B4
- 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