--- title: "Entropy as a State Function" description: "Entropy is a state function. Find its change by adding small reversible heat transfers divided by their temperatures along a path between states. This sum is zero around a closed reversible loop. An i" canonical: https://lightmysky.com/learn/science/entropy-as-a-state-function-mt_bg_K5nU-GZ source: https://lightmysky.com/learn/science/entropy-as-a-state-function-mt_bg_K5nU-GZ.md retrieved: 2026-11-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Entropy as a State Function Entropy is a state function. Find its change by adding small reversible heat transfers divided by their temperatures along a path between states. This sum is zero around a closed reversible loop. An isolated system's total entropy cannot decrease. Subject: Science · Area: Thermal & Statistical Physics · Ages 19 to 21 Page: https://lightmysky.com/learn/science/entropy-as-a-state-function-mt_bg_K5nU-GZ ## Ready when they can - Computes the entropy change for a reversible isothermal process and for a heated solid - Shows that a complete cycle has zero net entropy change and explains heat/T cancellation around a reversible cycle - Finds the entropy change of the surroundings and argues that the total cannot fall ## Lesson: Entropy changes depend on the states Entropy S is a state function: its change depends on the initial and final equilibrium states. Choose a reversible path and add each small heat transfer divided by its temperature in kelvin. At constant temperature, delta S = Qrev/T. Heat absorbed is positive; heat released is negative. For an irreversible process, use a reversible path between the same states. Its actual heat divided by temperature need not give its entropy change. **Example.** Let 20 g of ice melt at 273.15 K, taking 6680 J from a reservoir held at 293.15 K. The water stays at the melting temperature. A reversible melting path gives an ice entropy gain of 6680/273.15, about 24.46 J/K. The reservoir loses 6680/293.15, about 22.79 J/K. Their sum rises by about 1.67 J/K. The bars compare gain and loss magnitudes; the loss enters the sum with a minus sign. Any complete cycle restores the working substance's initial state, so its net entropy change is zero, even if the cycle is irreversible. For a reversible cycle, the sum of reversible heat/T is also zero. Follow one reversible route from A to B, then reverse another route to return to A. The zero loop sum makes the two forward-route sums equal. This establishes path independence. *(drawing: Reversing the second route changes the sign of its entropy change.)* For a solid with constant heat capacity C and no phase change, a small reversible temperature rise dT needs heat C dT. Adding C dT/T gives delta S = C ln(Tf/Ti). Ti and Tf are initial and final temperatures in kelvin; ln means natural logarithm. Heating gives a positive result and cooling a negative one. If heat capacity varies, add the small heat/T contributions instead of treating C as constant. The second law applies to an isolated system, including all affected surroundings. Add the entropy changes of every part. The total is zero for a reversible process and positive for an irreversible process; it cannot be negative. One part may lose entropy if the other parts gain at least as much. A reservoir held at temperature T has entropy change Q/T, with Q positive into that reservoir. **Recap.** Calculate entropy change along a reversible path. A cycle has zero net change. For an isolated whole, including all affected surroundings, total entropy cannot decrease. *The teaching and question repairs were written for this dataset. OpenStax entropy material was consulted for facts; its prose and figures are not reproduced.* ## Practice 8 questions on this page, each with its working shown. ## Needs first - [The Carnot Cycle and the Ceiling on Efficiency](https://lightmysky.com/learn/science/the-carnot-cycle-and-the-ceiling-on-efficiency-mt_aWH0BHM556) ## Optional connections - [Entropy and the Spread of Energy](https://lightmysky.com/learn/science/entropy-and-the-spread-of-energy-mt_a_2feH2gnE) ## Opens up - [Microstates, Multiplicity and Boltzmann's Entropy](https://lightmysky.com/learn/science/microstates-multiplicity-and-boltzmanns-entropy-mt_55I3VvYMc6)