Two rigid, thermally insulated containers each have a volume of and initially contain…

CHEMISTRY · Multi-part · CBSE · Chemistry · Thermodynamics · Thermodynamics

Problem

Two rigid, thermally insulated containers each have a volume of

2.0\,\text{L}

and initially contain gas at

300\,\text{K}

and

1.0\,\text{atm}

. In Scenario 1, container 1 holds pure nitrogen and container 2 holds pure oxygen. In Scenario 2, the partition between the two containers is removed so that the same total amount of gas (still

2.0\,\text{L}

in volume) is now a uniform mixture of nitrogen and oxygen at

300\,\text{K}

and

1.0\,\text{atm}

. No heat exchange with the surroundings occurs in either scenario. (a) Indicate which scenario has the greater entropy for the gas and explain why. (b) The containers plus their contents constitute an isolated system. Discuss whether the second law of thermodynamics permits a spontaneous change from Scenario 2 back to Scenario 1. Support your answer with entropy considerations. (c) If the temperature of the mixed gas in Scenario 2 were increased to

600\,\text{K}

at constant volume, predict qualitatively how the entropy would compare with the entropy in Scenario 1 at

300\,\text{K}

and justify your prediction.

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