Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature T₀, 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 reac…

Question

Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature T₀, 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 T_f in terms of T₀ is

Accepted Answer

(4) T_f = 3/2 T₀. The boxes are rigid, so no work is done and the total internal energy is conserved. Nitrogen is a rigid diatomic: C_V=5/2 R. Helium is monoatomic: C_V=3/2 R. Energy before: 5/2 RT₀+3/2 R(7/3 T₀)=5/2 RT₀+7/2 RT₀=6RT₀. Total heat capacity: 5/2 R+3/2 R=4R. T_f=(6RT₀)/(4R)=3/2T₀.

Step-by-step solution

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