TS EAMCET · Physics · Waves and Sound

Consider an ideal gas in a closed container at $300 K .$ The container is then heated so that the average velocity of particles of the gas increases by a factor of $4 .$ What would be the final temperature?

A $4500 {}^{\circ}C$
B $4527 {}^{\circ}C$
C $4617 {}^{\circ}C$
D $4600 {}^{\circ}C$

Verified Solution

Answer & Solution

Correct Answer

(B) $4527 {}^{\circ}C$

Step-by-step Solution

Detailed explanation

We know the relation between absolute temperature and average speed of the molecule inside the container is, vavg∝T, it means, vavg1vavg2=T1T2⇒vavg14vavg1=300T2⇒T2=4800 K Now use the relation between centigrade scale and Celsius scale,…

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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Consider an ideal gas in a closed container at 300 K. The container is then heated so that the average velocity of particles of the gas increases by a factor of 4. What would be the final temperature?

Step-by-step Solution

Consider an ideal gas in a closed container at $300 K .$ The container is then heated so that the average velocity of particles of the gas increases by a factor of $4 .$ What would be the final temperature?