Heat from an infinite reservoir?

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Discussion Overview

The discussion revolves around the thermodynamic principles of a refrigerator operating between two reservoirs, specifically focusing on the heat transfer from a low temperature reservoir with infinite heat capacity. Participants explore how to express the heat flow from this reservoir in relation to work input and temperature differences.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant seeks to express the heat QL coming from the low temperature reservoir in terms of TL, TH, and W, noting that QL = CpdT is not applicable in this context.
  • Another participant clarifies that both reservoirs are assumed to have infinite heat capacity to maintain a steady-state with constant temperatures.
  • A different participant emphasizes that the hot reservoir does not have infinite heat capacity but maintains a constant temperature by losing heat at the same rate it receives heat from the refrigerator.
  • There is a suggestion that the cold reservoir operates similarly in an open system context.
  • One participant questions the concept of 'infinite capacity' by proposing alternative models, such as the Earth's precipitation cycle, while acknowledging that nothing is truly infinite.

Areas of Agreement / Disagreement

Participants generally agree on the assumption of infinite heat capacity for the low temperature reservoir, but there is disagreement regarding the implications of this assumption and the nature of the hot reservoir's heat capacity. The discussion remains unresolved regarding the specific equation for heat flow from the low temperature reservoir.

Contextual Notes

Participants have not fully resolved the implications of infinite heat capacity, and there are varying interpretations of how the reservoirs interact thermodynamically. The discussion includes assumptions about steady-state conditions and the nature of heat transfer in an open system.

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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