Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature To, while Box B contains one mole of helium at temperature (7/3) T0. The boxes are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases T1 , in terms of T0 is
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a
Tf=73T0
b
Tf=32T0
c
Tf=52T0
d
Tf=37T0
answer is B.
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Detailed Solution
When two gases are mixed together, thenHeat lost by the helium gas = Heat gained by the nitrogen gasnB×cvHe×73T0−Tf=nA×cvN2×Tf−T0 Box A 1 mole N2 Temperature = T0 Box B 1 mole He Temperature = 73T0 ⇒ 1×32R×73T0−Tf=1×52R×Tf−T0By solving, we getTf=32T0