TS EAMCET · Physics · Ray Optics

The mean free path for a gas at temperature $300 K$ and pressure $600$ torr is $10^{- 7} m .$ The mean free path of the gas at a temperature $400 K$ and pressure $200$ torr will be

A $2.5 \times 10^{- 8} m$
B $4.4 \times 10^{- 8} m$
C $3.3 \times 10^{- 8} m$
D $4 \times 10^{- 7} m$

Verified Solution

Answer & Solution

Correct Answer

(B) $4.4 \times 10^{- 8} m$

Step-by-step Solution

Detailed explanation

The mean free path in terms of pressure, λ=kT2d2P, here k is the Boltzmann constant, now make the proper relation between pressure and temperature of the gas, λ1λ2=kT12d2P1kT22d2P2=T1P1T2P2=T1P2P1T2=300×600400×200⇒10-7λ2=300×600400×20…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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The mean free path for a gas at temperature 300 K and pressure 600 torr is 10-7 m. The mean free path of the gas at a temperature 400 K and pressure 200 torr will be

Step-by-step Solution

The mean free path for a gas at temperature $300 K$ and pressure $600$ torr is $10^{- 7} m .$ The mean free path of the gas at a temperature $400 K$ and pressure $200$ torr will be