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?

#Mechanics

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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 - 3 years, 8 months ago

Hey Josh,

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

The gas gets heated and pressured by the compressor.
The heat dissipates through the radiator until the gas reaches room temp.
Despite losing all that heat, the gas still has higher than atmospheric pressure.
My understanding is that when heat is taken away from the gas, it loses pressure.
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 - 3 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$