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 options given below :

Both Statement I and Statement II are true

Statement I is false but Statement II is true

Statement I is true but Statement II is false

Both Statement I and Statement II are false

Heat and Thermodynamics PYQ — JEE Main 2024 · 8 Apr · Shift 2 · Q74 with Solution

View written solutionFree

Correct answer: B

Check Statement (I): Mean free path

For an ideal gas, the mean free path $\lambda$ is given by

\lambda = \frac{1}{\sqrt{2}\,\pi d^2 n}

where:

$d$ = molecular diameter
$n$ = number of molecules per unit volume

From this expression,

\lambda \propto \frac{1}{d^2}

So, the mean free path is inversely proportional to the square of molecular diameter.

Therefore, Statement (I) is true.

Check Statement (II): Average kinetic energy

The average kinetic energy of one gas molecule is

\bar{E} = \frac{3}{2}kT

where:

$k$ = Boltzmann constant
$T$ = absolute temperature

Thus,

\bar{E} \propto T

So, the average kinetic energy of gas molecules is directly proportional to absolute temperature.

Therefore, Statement (II) is true.

Choose the correct option

Statement (I): True
Statement (II): True

Hence, the correct option is:

\boxed{\text{B}}

Comparison with stored correct answer

Stored correct answer: $\text{B}$

My derived answer: $\text{B}$

They match.

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View written solutionFree

Correct answer: B

Check Statement (I): Mean free path

For an ideal gas, the mean free path $\lambda$ is given by

\lambda = \frac{1}{\sqrt{2}\,\pi d^2 n}

where:

$d$ = molecular diameter
$n$ = number of molecules per unit volume

From this expression,

\lambda \propto \frac{1}{d^2}

So, the mean free path is inversely proportional to the square of molecular diameter.

Therefore, Statement (I) is true.

Check Statement (II): Average kinetic energy

The average kinetic energy of one gas molecule is

\bar{E} = \frac{3}{2}kT

where:

$k$ = Boltzmann constant
$T$ = absolute temperature

Thus,

\bar{E} \propto T

So, the average kinetic energy of gas molecules is directly proportional to absolute temperature.

Therefore, Statement (II) is true.

Choose the correct option

Statement (I): True
Statement (II): True

Hence, the correct option is:

\boxed{\text{B}}

Comparison with stored correct answer

Stored correct answer: $\text{B}$

My derived answer: $\text{B}$

They match.

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