# 3.4.4: Sad Consequences of the Second Law


After the First Law has been discovered, some people started thinking: if heat is equivalent to mechanical work, we should be able to take a big reservoir of thermal energy – such as, e.g., an ocean – and extract work from it. There is so much thermal energy in any ocean that there should be enough mechanical work for everybody for thousands of years!

A machine that would extract thermal energy from oceans and convert it to usable work was given the name of Perpetual Motion Machine of the Second Kind (PMMoSK). The first kind was a machine that would produce work out of nothing.

Some inventors seriously believed that making such a machine would be possible. They spent much time working on projects and prototypes. The failure of all such efforts was certainly one of the factors that helped to discover the second law of thermodynamics.

Who has “derived” the Second Law? Not a human scientist. It was Mother Nature who decided that things should be that way. The role of human scientist was only that by analyzing a wide variety of facts they reached a firm conclusion that there is such a law of nature1.

A simple explanation why it is not possible to build a PMMoSK is presented in Fig. $$\PageIndex{1}$$. Consider an isolated homogeneous system. An amount of work $$\Delta W$$ can be added to it to increase its internal energy $$U$$ - the result is the same as if one added an equivalent amount of heat $$\Delta Q$$, so that the entropy of the system increases by $$\Delta S=\Delta W / T$$.

The increase of entropy is permitted by the Second Law, so everything is OK with the process. But not with an opposite one! Extracting a portion of work $$\Delta W$$ from the system would be equivalent with taking a portion of entropy $$\Delta S=\Delta W / T$$ away from it - so, in consequence, to lowering the system entropy, which is strictly forbidden by the Second Law.

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4In fact, other laws of physics were discovered in the same way. For instance, Newton did not “derive” his famous second law of dynamics, $$F = m a$$. By analyzing observations, he concluded that there is such a law of nature. And many generations of physicist later strengthened his conclusion by performing zillions of tests. Something derived by scientists may only be a theorem, not a law.

3.4.4: Sad Consequences of the Second Law is shared under a CC BY 1.3 license and was authored, remixed, and/or curated by Tom Giebultowicz.