Entropy as a State Function
Heat divided by temperature, summed round a reversible path, returns to zero, which means entropy is a property of the state. Real processes only ever increase the entropy of the whole system and its surroundings.
What a learner can do afterwards
- Computes the entropy change for a reversible isothermal process and for a heated solid
- Shows that entropy returns to its starting value round a reversible cycle
- Finds the entropy change of the surroundings and argues that the total cannot fall
1 · Read
Entropy is a property of the state, fixed by the current condition rather than the path taken. Its change along a reversible path is heat divided by temperature, summed step by step. Taking heat in raises it and giving heat out lowers it, with T always in kelvin.
Melt 50 g of ice at 0 C, which is 273 K, using 16.8 kJ of heat. The ice gains 16800 over 273, which is 61.5 J per K. The warm room giving that heat loses about 57.3 J per K, so the total climbs: the ice gains more than the room loses.
Round any reversible cycle the rises and falls cancel exactly, so the working substance returns to its starting entropy. That is why entropy is a state function: any two states differ by one fixed amount whatever reversible path joins them. For the whole closed world the total never falls, and irreversible steps raise it.
Always include the surroundings before judging the second law. A system part may fall in entropy while the total still climbs. Mind the sign: heat absorbed counts positive and heat released counts negative.
Entropy change is reversible heat over temperature, cycles return it to zero, and the world total never falls.
2 · Watch
Take it off screen
Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.