The mean free path of a gas molecule is lambda. If the temperature is doubled and the pressure is halved, what is the new mean free path?

C. 4 — The mean free path is proportional to T/P. If T becomes 2T and P becomes P/2, the ratio T/P becomes (2T)/(P/2) = 4(T/P), so the mean free path increases by a factor of 4.

JEE Main · PhysicsHard

$The mean free path of a gas molecule is λ = \frac{k T}{2 π d ^{2} P} . If the temperature T is doubled and the pressure P is halved, what is the new mean free path λ^{'} ?$

A. $λ$
B. $2 λ$
C. $4 λ$
D. $λ /4$

Show correct answer & step-by-step solution

Correct answer: C — $4 λ$

Solution

λ \propto \frac{T}{P} . λ^{'} \propto \frac{2 T}{P /2} = 4 \frac{T}{P} = 4 λ .

Attempt this question & track your score

Attempt & Track Free →

More Kinetic Theory of Gases practice questions

$According to the kinetic theory of gases, the average kinetic energy of a gas molecule is directly proportional to which$
$What is the value of the degrees of freedom for a monoatomic gas molecule?$
$The root mean square speed of gas molecules is given by which expression?$
$At what temperature will the root mean square speed of oxygen molecules be double its value at 27 degrees Celsius?$
$Which of the following assumptions is made in the kinetic theory of ideal gases?$
$Two identical containers contain helium and neon gas respectively at the same temperature and pressure. The ratio of the$
$A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature T. Neglecting vibrational modes, the tot$
$The mean free path of gas molecules depends on the diameter d of the molecules as$
$If the pressure of an ideal gas is doubled and the volume is halved, the temperature of the gas will$
$The ratio of the adiabatic exponent gamma for a mixture of 1 mole of a monatomic gas and 2 moles of a diatomic gas is$
$A mixture of two ideal gases with adiabatic exponents gamma1 and gamma2 and mole fractions x1 and x2 is kept in a contai$
$A vessel contains a gas at pressure P and temperature T. If the gas is replaced by another gas of molecular weight twice$

View all Kinetic Theory of Gases questions →

The mean free path of a gas molecule is λ=2​πd2PkT​. If the temperature T is doubled and the pressure P is halved, what is the new mean free path λ′?

Solution

Attempt this question & track your score

More Kinetic Theory of Gases practice questions

$The mean free path of a gas molecule is λ = \frac{k T}{2 π d ^{2} P} . If the temperature T is doubled and the pressure P is halved, what is the new mean free path λ^{'} ?$