Calculate the total change in entropy of the system and the surroundings
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the second law depends on the entropy change of everything, not just the system. It is possible for a process to occur that lowers the energy of the system, but raises the entropy of the surroundings. As long as the surrounding increase more than the system goes down, then this process will occur. Water freezing in a constant temperature surroundings at -5 °C is an example of this. The system (the water) will decrease in entropy first because its temperature will go down and second because it will go from a liquid to a solid. The entropy of the surroundings will increase since energy (heat) is flowing into the surroundings from the system.
How do we calculate entropy changes for the surroundings? In most cases, the surroundings will be at a constant temperature. Therefore the entropy change will simply be related to the amount of energy that enters the surroundings in the form of heat divided by the temperature of the surroundings. Since we typically give heat a sign based on the system, the heat from the perspective of the surroundings is equal to the heat of the system but opposite in sign. Heat flowing out of the system is flowing into the surroundings. Then entropy change of the surroundings is
ΔSsurroundings=qsurroundingsTsurroundings=−qsystemTsurroundingsΔSsurroundings=qsurroundingsTsurroundings=−qsystemTsurroundings
As heat is generally defined from the perspective of the system, the subscript "system" is often left off of the heat in the last version of this equation.
If we have the entropy changes of the system and surroundings, we can calculate total entropy change. The total entropy change is simply the sum of the system and the surroundings.
ΔStotal=ΔSsystem+ΔSsurrounding
the second law depends on the entropy change of everything, not just the system. It is possible for a process to occur that lowers the energy of the system, but raises the entropy of the surroundings. As long as the surrounding increase more than the system goes down, then this process will occur. Water freezing in a constant temperature surroundings at -5 °C is an example of this. The system (the water) will decrease in entropy first because its temperature will go down and second because it will go from a liquid to a solid. The entropy of the surroundings will increase since energy (heat) is flowing into the surroundings from the system.
How do we calculate entropy changes for the surroundings? In most cases, the surroundings will be at a constant temperature. Therefore the entropy change will simply be related to the amount of energy that enters the surroundings in the form of heat divided by the temperature of the surroundings. Since we typically give heat a sign based on the system, the heat from the perspective of the surroundings is equal to the heat of the system but opposite in sign. Heat flowing out of the system is flowing into the surroundings. Then entropy change of the surroundings is
ΔSsurroundings=qsurroundingsTsurroundings=−qsystemTsurroundingsΔSsurroundings=qsurroundingsTsurroundings=−qsystemTsurroundings
As heat is generally defined from the perspective of the system, the subscript "system" is often left off of the heat in the last version of this equation.
If we have the entropy changes of the system and surroundings, we can calculate total entropy change. The total entropy change is simply the sum of the system and the surroundings.
ΔStotal=ΔSsystem+ΔSsurrounding
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