Question

Consider a process where the entropy change of the system is negative. What can be inferred if the process is spontaneous?

• A. The entropy of the surroundings must decrease.
• B. The entropy of the surroundings must increase more than the decrease in the system.
• C. The total energy of the system increases.
• D. The system is in a closed cycle.

Hint:

Second Law of Thermodynamics. For spontaneous processes, \(\Delta S_{universe = \Delta S_{system + \Delta S_{surroundings>0\). If \(\Delta S_{system\) is negative, \(\Delta S_{surroundings\) must be positive and larger in magnitude for the process to be spontaneous.

Answer 1

The Correct Option is B

The second law of thermodynamics states that for a process to be spontaneous, the total entropy change of the universe (system + surroundings) must be positive (or zero for a reversible process at equilibrium).
$$ \Delta S_{universe} = \Delta S_{system} + \Delta S_{surroundings} $$ For a spontaneous process: $$ \Delta S_{universe}>0 $$ $$ \Delta S_{system} + \Delta S_{surroundings}>0 $$ We are given that the entropy change of the system is negative (\(\Delta S_{system}<0\)).
Let \(\Delta S_{system} = -x\), where \(x\) is a positive value.
Substituting into the spontaneity condition: $$ -x + \Delta S_{surroundings}>0 $$ $$ \Delta S_{surroundings}>x $$ This means that the entropy of the surroundings must increase (\(\Delta S_{surroundings}\) must be positive), and its increase must be greater in magnitude than the decrease in the entropy of the system (\(x = |\Delta S_{system}|\)).
Option (2) correctly states this condition.
Option (1) is incorrect.
Options (3) and (4) are irrelevant to the entropy criteria for spontaneity.