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

Question

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

Infinity Learn · Accepted Answer

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 $$getTf=32T0$$

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