Heat from an infinite reservoir?

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In the discussion, participants explore the concept of heat flow in a refrigerator system with a low temperature reservoir (TL) and a high temperature reservoir (TH), both assumed to have infinite heat capacity for steady-state operation. The primary focus is on expressing the heat QL extracted from the low temperature reservoir in relation to work input W and the temperatures TL and TH. Clarification is sought on how to derive an equation for QL, considering that the high temperature reservoir maintains a constant temperature by losing heat at the same rate it receives from the refrigerator. The conversation touches on the theoretical implications of infinite heat capacity and compares it to natural systems like the Earth's precipitation cycle, though acknowledging that nothing is truly infinite. The discussion emphasizes the need for a clearer mathematical representation of the heat transfer process in this thermodynamic scenario.
Dawei
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Hello,

For a refrigerator, if a low temperature (TL) reservoir has infinite heat capacity, what is the heat QL that is coming from it?

I have W = Qh - QL and I believe I know what Qh is, but I need a better way to express QL, something involving TL, TH, and/or W.

I know QL = CpdT, but obviously that does not help in this case...
 
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Can you please elaborate on your question more?
 
Hm, I guess it wasn't quite straightforward. It's just a simple refrigerator, pumping heat from a low temperature reservoir to a high temperature reservoir by inputting work W.

The low temperature reservoir has infinite heat capacity, the high temperature reservoir does not.

I'm trying to find an equation for the heat flowing from the low temperature reservoir.
 
Both reservoirs are assumed to have infinite heat capacity. That's the only way to achieve a steady-state with a constant temperature for each.

...so I'm not clear on what the issue is here either.
 
russ_watters said:
Both reservoirs are assumed to have infinite heat capacity. That's the only way to achieve a steady-state with a constant temperature for each.

The other reservoir, the hot one, does not have infinite heat capacity, it is maintaining a constant temperature because it is losing heat at the same rate that it is coming in from the refrigerator.
 
Dawei said:
The other reservoir, the hot one, does not have infinite heat capacity, it is maintaining a constant temperature because it is losing heat at the same rate that it is coming in from the refrigerator.
In that case, it's an open system - and the cold reservoir would work the same way.
 
Dawei said:
I'm trying to find an equation for the heat flowing from the low temperature reservoir.

Let H represent the hot temperature energy and L represent the low temperature energy.

H=L
 
What is the 'infinite capacity', a nuclear power plant?
Is the evaporation and condensation of the precipitation cycle not a simpler model for the formula?
The Earth supplies the infinite heat, the atmosphere the infinite cooling and it rains all the time.
[However none of the above is truly 'infinite'.]
 

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