Minimum work needed to compensate for a heat leak

In summary: You need to use the specific heat of the materials at their respective temperatures to calculate the work needed. Also, don't forget to take into account the change in temperature when calculating the work. In summary, the conversation discusses the search for high temperature superconductors and the potential cost savings in using them compared to older superconductors. The minimum work needed to compensate for a heat leak of 1 kJ into the superconductor is calculated using the first law of thermodynamics and the specific heat of liquid nitrogen and helium. However, the calculation is incorrect and needs to be redone using the specific heat of the materials at their respective temperatures.
  • #1
Muthumanimaran
81
2

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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  • #2
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?
 
  • #3
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
 
  • #4
No, you can't do that.
 

What is the definition of "Minimum work needed to compensate for a heat leak"?

"Minimum work needed to compensate for a heat leak" refers to the amount of work that must be done in order to prevent a loss of heat from a system due to a heat leak. It is the minimum amount of energy required to counteract the effects of the heat leak and maintain a desired temperature.

How is the minimum work needed to compensate for a heat leak calculated?

The minimum work needed to compensate for a heat leak is calculated using the Second Law of Thermodynamics, which states that heat will flow spontaneously from a warm object to a cooler one. This means that in order to maintain a constant temperature, work must be done to counteract any heat loss due to a heat leak.

What factors affect the minimum work needed to compensate for a heat leak?

The minimum work needed to compensate for a heat leak is affected by several factors, including the temperature difference between the system and its surroundings, the rate of heat transfer, and the efficiency of the heat transfer mechanism.

Why is it important to minimize the work needed to compensate for a heat leak?

Minimizing the work needed to compensate for a heat leak is important because it reduces energy consumption and cost. The less work that is needed to maintain a desired temperature, the more efficient and sustainable the system will be.

How can the minimum work needed to compensate for a heat leak be reduced?

The minimum work needed to compensate for a heat leak can be reduced by using effective insulation, choosing materials with low thermal conductivity, and implementing efficient heat transfer mechanisms. Regular maintenance and repairs can also help reduce the amount of work needed to compensate for a heat leak.

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