Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at a 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, Tf, in terms of T0 is :
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a
Tf=32T0
b
Tf=52T0
c
Tf=37T0
d
Tf=73T0
answer is A.
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Detailed Solution
Let final temperature be Tf thenTf=n1C V1T1+n2CV2T2n1CV1+n2CV2=(1)52R(T0)+(1)32R73T0(1)52R+(1)32R=32T0
Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at a 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, Tf, in terms of T0 is :