Minimum work needed to compensate for a heat leak

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Homework Help Overview

The discussion revolves around calculating the minimum work required to compensate for a heat leak of 1 kJ into superconductors, specifically comparing "high temperature" superconductors with older ones that operate at lower temperatures. The context involves thermodynamic principles, particularly the first law of thermodynamics, and the implications of operating temperatures on energy efficiency.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are exploring the application of the first law of thermodynamics to determine the work needed to counteract a heat leak. There are questions regarding the correct treatment of energy units and the initial conditions of the systems being analyzed.

Discussion Status

The discussion is ongoing, with some participants questioning the accuracy of previous calculations and the assumptions made regarding the temperatures of the superconductors. There is an indication of differing interpretations about how to approach the problem, particularly concerning the energy dynamics involved.

Contextual Notes

Participants are noting the importance of consistent unit usage and the initial temperature conditions of the superconductors, which are critical to the calculations being discussed. The discussion reflects a need for clarity on these foundational aspects before progressing further.

Muthumanimaran
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Homework Statement


A great deal of effort has been expended to find “high temperature superconductors”: materials that are superconductors at temperatures higher than the boiling point of liquid nitrogen (77 K). Most of the older superconductors had to be operated with liquid helium (boiling point 4.2 K) as the cooling fluid. To estimate the savings possible in operating costs through the use of the “high temperature” superconductors, calculate the minimum work needed to compensate for a heat leak of 1 kJ into the superconductor for both “high temperature” superconductors and the older ones. Assume that the ambient temperature is 300 K.

Homework Equations


First law of Thermodynamics
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The Attempt at a Solution


Minimum work needed to compensate heat leak, so the first law of thermodynamics says

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so

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The specific heat for Liquid Nitrgoen is
kgK.gif


gif.latex?W%3D454.gif


for ordinary superconductor, for liquid helium
kg%20K.gif


gif.latex?W%3D%283.12%5Ctimes10%5E3%29%28300-4.gif


gif.latex?W%3D922.gif

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That is not the right answer, and if you would have worked with units consistently you would have seen the problem.

The systems you should consider are at the temperatures of liquid nitrogen or helium already. Now 1 kJ of energy is added to this cold reservoir. How much work do you need to remove this 1kJ?
 
mfb said:
That is not the right answer, and if you would have worked with units consistently you would have seen the problem.

The systems you should consider are at the temperatures of liquid nitrogen or helium already. Now 1 kJ of energy is added to this cold reservoir. How much work do you need to remove this 1kJ?
same 1kJ of work
 
No, you can't do that.
 

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