How can I calculate the temperature of a body between two thermal reservoirs?

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Discussion Overview

The discussion revolves around calculating the temperature of a body that is in contact with two thermal reservoirs at different temperatures. Participants explore the theoretical framework and practical application of heat transfer principles, particularly focusing on the conditions for equilibrium and the behavior of temperature distribution within the body.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant suggests that knowing the temperatures of the reservoirs, the area of contact, and the coefficients of conduction should allow for the calculation of the body's equilibrium temperature.
  • Another participant recommends looking up Fourier's law as a potential resource for understanding heat transfer.
  • A participant expresses difficulty in applying Fourier's law to determine the temperature of the object despite reviewing related materials.
  • It is proposed that the steady state must be established, where the heat entering from the hot reservoir equals the heat leaving to the cold reservoir.
  • One participant notes that the temperature within the body will not be uniform but will vary monotonically from the high temperature end to the low temperature end.
  • A later reply clarifies that the assumption of internal equilibrium is necessary; otherwise, solving the heat equation is required.

Areas of Agreement / Disagreement

Participants generally agree on the need to consider the steady state and the non-uniform temperature distribution within the body. However, there is no consensus on the specific methods or equations to apply for calculating the temperature.

Contextual Notes

Participants mention the need for assumptions regarding internal equilibrium and the implications of solving the heat equation, which remain unresolved in the discussion.

Noahfoose
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If I know the temperatures of the two thermal reservoirs (one hot, one cold), the area of contact between each reservoir and the body, and the coefficients of conduction, it seems like I should be able to calculate the equilibrium temperature of the body, but I can't seem to figure out how.
 
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Thanks for the tip! I've been looking through that wikipedia page and some information on thermopedia but I'm still a little lost on how I can use that law to determine the temperature of the object
 
You need to figure out the steady state, where heat entering the system from the hot reservoir equals heat leaving the system to the cold reservoir.
 
The temperature is not going to be uniform. It is going to vary monotonically from the high temperature end to the low temperature end.

Chet
 
Chestermiller said:
The temperature is not going to be uniform. It is going to vary monotonically from the high temperature end to the low temperature end.

Chet
Right. I should've mentionned that I was assuming internal equilibrium. Otherwise, you need to solve the heat equation.
 

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