# Why does entropy allow heat to be converted to work?

Physical chemistry has made me question everything.

Recently, I was thinking: "why is it even possible to convert heat to work?"

From what I learned, a heat engine can take energy in and convert it into work. However, heat can be defined as more "disordered" than work (because in heat, particles are more "random", but in work, they more "organized". Let me know if you'd like for me to elaborate).

So, if heat is more disordered, having more heat and less work means that there is greater entropy. Therefore, when we convert heat to work, we are decreasing the entropy, are we not? And it's not just the entropy of the system, but the universe (because we obtain the heat from the surroundings).

So, if according to the 2nd law, entropy can only increase, how is it possible to convert heat to work? What am I understanding wrong?

• Entropy can only increase overall. But it's possible to reduce entropy in one region of space if you're increasing entropy by more somewhere else at the same time. Sep 27 '19 at 21:37
• See the latest update to my answer. If you need further clarification, I'd be happy to provide it. Hope it helps. Sep 27 '19 at 22:15

From what I learned, a heat engine can take energy in and convert it into work. However, heat can be defined as more "disordered" than work (because in heat, particles are more "random", but in work, they more "organized". Let me know if you'd like for me to elaborate U

You learned correctly.

Therefore, when we convert heat to work, we are decreasing the entropy, are we not?

Once again you are correct. However, a heat engine operating in a cycle can only convert part of the incoming heat from a high temperature source into work. It must discard the other part of the incoming heat to a lower temperature environment. One version of the second law is it is impossible to operate an engine in a cycle where it exchanges heat with only one temperature reservoir and converts it completely into work. There must always be heat discarded to a lower temperature reservoir.

So, if according to the 2nd law, entropy can only increase, how is it possible to convert heat to work? What am I understanding wrong?

What you understand wrong is you are not taking into account the increase in entropy of the surroundings due to the necessity of heat being discarded to the surroundings. Yes, the heat the engine takes from the high temperature environment decreases the entropy of the high temperature environment (turns disordered energy into ordered energy- i.e, work). But the heat discarded to the low temperature environment increases the entropy of the low temperature environment.

For all real (irreversible) cycles the increase in entropy of the environment due to the discarded heat is greater than the decrease in entropy of the environment due to taking heat from the environment to do work. Since for any complete cycle the entropy change of the system (heat engine) is zero, the overall change in entropy of the universe (system + environment) will be greater than zero.

The best you can do is for a reversible cycle, where the overall change in entropy is zero. The most efficient of the reversible cycles operating between two constant temperature reservoirs is the Carnot cycle.

If you need a specific example, I can amend my answer.

Hope this helps.

• "... the increase in entropy of the environment due to the discarded heat is greater than the decrease in entropy of the environment due to taking heat from the environment to do work..." - Excellent explanation, makes a lot of sense. Thanks a lot! Sep 27 '19 at 22:16
• @F16Falcon You are very welcome. Glad it helped. Sep 27 '19 at 22:17
• @F16Falcon, think of it this way. It's not so important that heat is more disordered than work (whatever that may mean). Energy of any form is conserved, but if you have a heat engine available, and you can "drop" high temperature heat through a big temperature difference, you can get useful work out of that energy as it loses temperature. That temperature difference is absolutely required is you want to turn some of the heat into work. Sep 28 '19 at 1:13
• @DavidWhite You're absolutely correct, however, I was wondering about the entropy aspect of the concept, rather than actually the "physical mechanism" for how heat can become work. Apologies, my title may not have made that quite clear. I'll modify it. Sep 28 '19 at 1:33
• "It must discard the other part of the incoming heat to a lower temperature environment" This line confuses me. It sounds like you're saying "every time you take a shot, you have to spill some vodka for the gods." How is this "enforced" in a manner of speaking? What's to keep you from using all the energy to do work, and skipping the spilled shot? Where in the system does this fail, or asymptote to a halt?
– Tal
Jun 10 '20 at 4:38