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Refrigerator explanation question

From this page: https://brilliant.org/practice/how-does-a-refrigerator-work/?p=9

I am confused about this part:

  • This gas is then compressed at the pump, raising its temperature and pressure.
  • After exiting the compressor, this gas cools to room temperature in the external radiator, maintaining its high pressure.

Given the ideal gas law (PV = nRT), I don't understand how the gas maintains its high pressure while being cooled to room temperature? Is it simply that it's compressed so much that, even as it loses some pressure as it cools, it's still at a higher than atmospheric pressure?

Note by Jonah G
2 weeks, 2 days ago

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Hey Jonah, two things to be careful of. One is that the ideal gas law assumes no heat is being added to or removed from the gas. In the refrigerator cycle there are several places where this is happening. The second thing is that not only can temperature change with position, but the number density \(n\) as well. This isn't to say that the profile along the tube is so simple so as to be constant with position, but you can certainly have a gas at constant pressure so long as \(T(x)\) and \(n(x)\) maintain a constant product.

Josh Silverman Staff - 2 weeks ago

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Hey Josh,

Thanks for your answer. Bear with me, I'm still a bit confused. Which step am I misunderstanding?

  1. The gas gets heated and pressured by the compressor.
  2. The heat dissipates through the radiator until the gas reaches room temp.
  3. Despite losing all that heat, the gas still has higher than atmospheric pressure.
  4. My understanding is that when heat is taken away from the gas, it loses pressure.
  5. Given 4, it still seems to me that we're missing an explanation of why the gas retains it's extra pressure (or at least enough of it) despite losing lots of heat.

Jonah

Jonah G - 2 weeks ago

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