Minimum work needed to compensate for a heat leak

[Muthumanimaran]

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

The Attempt at a Solution

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

so

The specific heat for Liquid Nitrgoen is

for ordinary superconductor, for liquid helium

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[mfb]

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?

 

[Muthumanimaran]

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

 

[mfb]

No, you can't do that.