## Friday, August 27, 2010

### Heat engines

Before I make my post, I’d like to draw our attention to the ‘Volunteer Needed’ post made by Ross. I meant to bring this up at the meeting on Wednesday, but I forgot. I will be at university working on my BIPH3000 project on Thursday afternoon, so I will be around at the time of this meeting. I would rather continue to work on my project at that time, but if it is not convenient for anyone else to make, I will volunteer to attend this meeting on our behalf. Let me know if any of you would rather do this though.

This chapter is complex. I think I’d understand the derivations better if all the variables for a specific measurement, like entropy, were made explicit, and proper partial derivatives were taken. I have trouble understanding what equations that look like dS=dq/T mean. However there was one part I found quite easy to understand, and that was the comparison of the biosphere to a heat engine (section 3.5.4). A heat engine is a physical system that converts heat energy to mechanical energy. This concept sounds heretical in the context of the first chapter, which suggest that heat energy is the lowest form of energy; energy can change forms, but each time the energy changes form, some of it is inevitably lost as heat energy. So a heat engine seems to suggest there is a way to convert this heat energy back into useful energy.

However, heat engines can exist. While heat is being converted to a useful form of energy, something is being irreplaceably lost: the order of the system. For a heat engine to work there must be two thermal reservoirs of different temperatures. Whatever the action of the motor is, the motor cycle has 4 necessary stages. Initially, heat energy from the warmer reservoir must be applied to another component. This component then uses the heat energy to increase its entropy, which then can be used to perform work. For the cycle to be repeatable, the component must be cooled down again, so the component is removed from contact with the warm reservoir and placed in thermal contact with the cooler reservoir. Decreasing the temperature decreases the entropy, so the component’s entropy and temperature is restored to the original state. The final step is the component is moved from the cool reservoir to the warm one again.

During this cycle, heat is transferred from the warm reservoir to the cooler one. This is where there irreversible exchange is occurring. Once enough heat energy is removed from the warmer reservoir to the cooler one to make the temperature of the reservoirs equal, there is no way to return the heat to the warmer reservoir from the cooler one (without performing work from outside the system). So what was learnt in the first chapter was not violated: heat can be made to do some useful work, but some order is lost (in this case, the original ordered distribution of heat energy).

I liked that this section was also compared to the biosphere. I don’t think the analogy is exactly true, as it is not just heat energy that the sun is radiating, and it is especially not the heat energy that is exciting the electrons in chlorophyll. But the comparison does make it easier to understand how the sun can (potentially) cause order on the rest of the solar system, as the distribution of solar energy in the solar system is at very low entropy.

#### 3 comments:

1. hey mitch, i'll go to the meeting, I have to kill some time before headed off to my dance lesson that night anyways

2. Cool. Thanks for replying.

3. No worries.
Now, in response to the actual part of your post. The heat engine is such an interesting process, yet so simple. As you said, both a warm and cool thermal reservoir are used, and simple thermal exchange is applied. First as you said to the component from the warm, then from the component to the cool, and then creating equilibrium between the two resevoirs.and this cycle is completely repeatable with new sets of reservoirs. what is also cool about this process is that if any energy is lost as heat, it just goes right back into the system and effectively used again, or lost and regained again until it is used.