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Question

Calculate the temperatures at which the root mean square velocity, average velocity and most probable velocity of oxygen gas are all equal to 1500 ms1:

A
TRMS=2886K,Tav=3399K,Tmp=4330K
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B
TRMS=3399K,Tav=2886K,Tmp=4330K
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C
TRMS=3399K,Tav=4330K,Tmp=2886K
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D
None of these
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Solution

The correct option is A TRMS=2886K,Tav=3399K,Tmp=4330K
(a) THe expression for the RMS speed is URMS=3RTM
Substitute values in the above expression.
1500=3×8.314×TRMS32×103
Hence, TRMS=2886K
(b) The expression for the average speed is Vav=8RTπM
Substitute values in the above expression.
1500=8×8.314×Tav3.1416×32×103
Hence, Tav=3399K
(c) The expression for the most probable speed is αmp=2RTM
Substitute values in the above expression.
1500=2×8.314×Tmp32×103
Hence, Tmp=4330K

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