Entropy and system evolution

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The **disorder** of a system — the **number of microstates** (microscopic arrangements) available. Unit: **J K⁻¹**.

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One specific microscopic arrangement of the particles that gives the same overall (macroscopic) state. **More microstates ⇒ higher entropy**.

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$\Delta S = \dfrac{\Delta Q}{T}$, with **T in kelvin**.

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$\Delta S$ in **J K⁻¹**, $\Delta Q$ in **J**, $T$ in **K**.

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Heat **in** ⇒ ΔQ is **positive** (entropy rises); heat **out** ⇒ ΔQ is **negative** (entropy falls).

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The **entropy of an isolated system never decreases** — it increases for any irreversible (real) process.

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Yes — but only if another part gains **more**, so the **total** entropy of the isolated system still does not decrease.

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Because it **increases the total entropy** of the universe ($\Delta S_{total} > 0$); the reverse would decrease it, so it never happens unaided.

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The **direction** of time set by the second law: real processes always run the way that **increases total entropy**.

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Calculate $\Delta S_{total}$ for the isolated system. If it is **positive**, the process can occur (and is irreversible).

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$\Delta S = \Delta Q/T$, and the **cold** body has the **smaller T**, so for the same ΔQ it gains **more** entropy than the hot body loses.

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Entropy is the **joule per kelvin (J K⁻¹)**; energy is the **joule (J)** — do not confuse them.