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

Question

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

Accepted Answer

Correct answer: B. (b) Given, Initial temperature of container, Ti=300 K Let vi and vf be the initial and final velocity of particle. where, vf=4 vi and final temperature of container be Tf As we know that, Average velocity, v_ av= 8 RT πm. Here R is universal gas constant, T is temperature and m be molar mass. On squaring both sides, we get v_ av^2= 8 RT πm ⇒V_ av^2 ∝T ∴ ( V_FV_i )^2= ( T_FT_i ) ⇒ ( 4V_i^2V_i )= ( T_1T_i ) ⇒16 Ti= Tf ⇒ Tf=16 300=4800 K ∴ Tf= (4800-273 )^ C=4527^ C .

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

Solution

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