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The mean free path of a gas molecule is λ1 at temperature T. The pressure and temperature, of both the gas, are made two times their original value. The new mean free path was found to be λ2. Then λ12 is -
  • a)
    1:2
  • b)
    2:1
  • c)
    1:1
  • d)
    None of the above
Correct answer is option 'C'. Can you explain this answer?
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Mean Free Path and its Relation to Pressure and Temperature:
The mean free path of a gas molecule is a measure of the average distance a molecule travels between collisions with other molecules. It is denoted by λ and is inversely proportional to the pressure and directly proportional to the temperature of the gas.

Relation between Mean Free Path and Pressure/Temperature:
- When the pressure and temperature of a gas are doubled, the mean free path of the gas molecules also changes.
- If the original mean free path is λ1 and the new mean free path is λ2, the relationship between them can be expressed as:
λ1 / λ2 = 1 / 1
This implies that the ratio of the original mean free path to the new mean free path is 1:1.
Therefore, the correct answer is option 'C' - 1:1. This means that when the pressure and temperature of a gas are both doubled, the ratio of the original mean free path to the new mean free path remains the same at 1:1.
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The mean free path of a gas molecule isλ1at temperature T. The pressure and temperature, of both the gas, are made two times their original value. The new mean free path was found to beλ2. Thenλ1:λ2is -a)1:2b)2:1c)1:1d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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