A) \[\Delta {{S}_{system}}>0\] only
B) \[\Delta {{S}_{surroundings}}>0\] only
C) \[\Delta {{S}_{system}}+\Delta {{S}_{surroundings}}>0\]
D) \[\Delta {{S}_{system}}-\Delta {{S}_{surroundings}}>0\]
Correct Answer: C
Solution :
\[\Delta {{S}_{system}}+\Delta {{S}_{surroundings}}>O\](for spontaneity) Because of \[\Delta S=R\ln \frac{{{V}_{2}}}{{{V}_{1}}}\] Here the volume of gas increase from \[{{V}_{1}}\] to \[{{V}_{2}}\] at constant temperature T. The total increase in entropy of the system and its surrounding during the spontaneous process of expansion considered above is, thus\[R\,\ln \,\left( \frac{{{V}_{2}}}{{{V}_{1}}} \right)\] since \[{{V}_{2}}>{{V}_{1}}\] it is obvious that the spontaneous (irreversible) isothermal expansion of a gas is accompanied by an increase in the entropy of the system and its surrounding considered together. \[\Delta {{S}_{system}}+\Delta {{S}_{surroundings}}>0\].
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