The Second Law

• The idea that entropy is not conserved is an idea that many students will have difficulties with
• Be ready to answer questions about where the other entropy comes from

Second Law and Entropy If you drop a hot chunk of metal into a cup of water, which way will energy be transferred by heating? What is the rule that governs this?

Why can't two objects that are at the same temperature spontaneously change temperature?

The second law of thermodynamics clarifies this rule, and extends it to cases where there might be other things going on, e.g. in the case of a refrigerator. The second law involves the change in entropy, which I defined for you previously: $$\Delta S = \int \frac{đ Q_{quasistatic}}{T}$$ The Second Law of Thermodynamics simply states that for any possible process, the change in entropy of a system plus its surroundings is either positive or zero. $$\Delta S_\text{system} + \Delta S_\text{surroundings}\ge 0$$ This law famously gives the “arrow of time,” meaning that it is the physical law that tells us which things can happen “forwards” but not “backward.” One handy trick when considering any process is to ask yourself if the precise reverse could happen. If it couldn't, then you can safely conclude that the entropy of the system plus its surroundings must have increased.

Other views if the Second Law We've already looked at the Second Law of Thermodynamics: $$\Delta S_\text{system} + \Delta S_\text{surroundings}\ge 0$$ As it turns out, there are several ways to state this law, and even more ways of understanding it. The Kelvin formulation states that:

• No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.

This is sometimes phrased in a colloquial way as:

• You cannot make a perfect engine.

There is also the Clausius formulation of the Second Law, which states that:

• No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature.

This is sometimes phrased in a colloquial way as:

• You cannot make a perfect refrigerator.

Both of these formulations are actually equivalent to the definition we gave above. These formulations also make it clear that if you could violate the Second Law, you could become filthy rich. You would have both a free source of energy, and at the same time a free source of refrigeration. The connection between these very different ways of looking at (and thinking about) the Second Law lies in the idea of a heat engine.