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Qrev is the heat being transferred into or out of the system. If heat is leaving the system, the q would be negative. If heat enters the system, then q is positive. This makes sense since if there is more energy in the system, you can expect there to be an increase in entropy.
It might help to think of it using the familiar concept q(system)=-q(surroundings). A system's surroundings gain the heat that a system loses. Because a gain in heat is an increase or positive value, the system must have the opposite sign when it loses heat. So if heat is leaving a system, q will be negative.
When qrev is negative, it means that the system is losing heat, so the surroundings will gain heat and vice versa if qrev is positive. You can think of it in the context of exothermic and endothermic: if a system is endothermic (taking in heat), then qrev will be positive and if a system is exothermic (releasing heat), then qrev will be negative.
The sign of delta S depends on the direction of heat flow. Delta S is simply qrev divided by T. qrev is negative whenever the system is losing heat. From that information, you then know that the surroundings gain heat. If the system is gaining heat, then qrev is positive.
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