Minimum work needed to compensate for a heat leak

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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