What Is the Second Law of Thermodynamics?

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where $\Delta Q$ is the thermal energy transferred to the system and $T$ is the absolute temperature in kelvin. A positive $\Delta Q$ means that the system receives energy as heat.

When energy transfers spontaneously from a hotter body to a colder body, the hot body's entropy decreases, but the cold body's entropy increases by a greater amount. Therefore, the total entropy increases, making the transfer irreversible.

For example, suppose $100\,\text{J}$ transfers from a reservoir at $400\,\text{K}$ to one at $300\,\text{K}$:

Therefore,

The positive total change shows that the process is permitted by the second law. The reverse transfer would decrease total entropy, so it cannot occur spontaneously without external work.

A common misconception is that entropy can never decrease. It can decrease locally in a non-isolated system, but this must be accompanied by an equal or greater entropy increase in the surroundings. The second law applies to the combined total.

Exam Technique

For an Explain question, link the direction of thermal energy transfer to the entropy changes of both bodies, then state the effect on total entropy. For a calculation, show each substitution, use temperature in kelvin, include units of $\text{J K}^{-1}$, and distinguish the system's entropy from the total entropy of the system and surroundings.