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What is an intuitive explanation for the concept of heat pumps? I know that it is basically a reversed Carnot process. We can for example take an amount of heat $Q_1$ out of a warmer system and transform part of it into work W. The rest goes to the colder system. If we now reverse that process we need to take heat out of the colder system. For this to be done we need the same amount of energy W we got out of the process previously. But here my problem starts: How do you force the energy to come out of the colder reservoir? How can you explain that without just saying that it is an inversed Carnot process?

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You describe the process. For an example, you might think of how a gas refrigerator works. You take a gas and expose it to the cold area, which cools it to the cold temperature. Then you isolate it from the cold area, which costs no energy. You compress it, raising the temperature above that of the hot reservoir, at the cost of physical work. You then connect it to the hot reservoir and let some heat escape. Disconnect it again, then expand it to a temperature below the cold reservoir, recovering some energy in the process. Now connect it to the cold reservoir and you have a cycle with work in and heat moving from cold to hot. This is really just adding details to saying an inverse of the Carnot process.

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  • $\begingroup$ So to summarize you can say that because heat only flows from the warmer to the colder system, we just play with the pressure to get a temperature difference which makes the heat flow... $\endgroup$ – Quasar Aug 12 '16 at 7:12
  • $\begingroup$ Exactly. That is where the work goes to move the heat from the cold place to the hot place. $\endgroup$ – Ross Millikan Aug 12 '16 at 7:21
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    $\begingroup$ That was actually pretty simple. It's important to note the difference between heat and temperature. $\endgroup$ – Quasar Aug 12 '16 at 7:25
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    $\begingroup$ @Quasar Indeed. Also, I think what was troubling you was the abstract description. You seem to understand the abstract idea that the inverted Carnot cycle must require work and all the proportions of the heat flows and work inputs must be the same (but opposite sign) of those for the heat engine, otherwise you could use the pair to violate the postulate that heat can't spontaneously flow from cold to hot. That's an elegant, general argument, and perhaps now you see a pattern that might be useful for your physics learning: if you think you understand a general principle like the above ..... $\endgroup$ – Selene Routley Aug 12 '16 at 7:32
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    $\begingroup$ ..... Carnot argument, next play around with physical imagination a bit and see whether you can think of a thought experiment as Ross has done that either illustrates the principle, or study in detail how the general, abstract ideas apply to your physical example. You find the two tend to strengthen one another as concepts in your mind, and you often see subtleties in the abstract arguments that you haven't seen before. At least, that's my experience. $\endgroup$ – Selene Routley Aug 12 '16 at 7:34
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You use a pump on a separate fluid (gas) system which is connected to the freezer (for example). The pump lowers pressure while the pipe system controls the volume of the fluid gas, and then this fluid can reach a smaller temperate than the internal of the freezer.

The freezer thus passes heat to the fluid system and cools down. The fluid cycles through the pipes to a part with higher pressure etc, which let it raise its temperature, so it can send away the heat to the surroundings.

The issue here is, that this pump performs an amount of work, and this is where $W$ enters the equation.

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