Problem with units for conduction rate?

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SUMMARY

The discussion centers on calculating the conduction rate through a copper slab using the formula Pcond = Kc * A * (TH - TC) / L. Given parameters include L = 25.0 cm, A = 90.0 cm², TH = 125°C, and TC = 10.0°C. The thermal conductivity K is specified as 401 W/m·K. The confusion arises from the treatment of temperature units, where the difference in temperature (TH - TC) yields the same numerical result in both Celsius and Kelvin, leading to a calculated conduction rate of 5774 W, which aligns with textbook answers.

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  • Understanding of heat conduction principles
  • Familiarity with the formula for conduction rate Pcond
  • Knowledge of thermal conductivity (K) and its units
  • Basic grasp of temperature scales (Celsius and Kelvin)
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L_landau
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Homework Statement


Consider the slab shown in Fig. 18-18. Suppose that L 25.0 cm, A 90.0 cm2, and the material is copper. If TH 125 C, TC 10.0 C, and a steady state is reached, find the conduction rate through the slab.

Homework Equations


Pcond = Kc *A*(TH - TC)/L
K = 401 W/m*k

The Attempt at a Solution


I'm converting degrees celsius to kelvin so that it cancels with the kelvin unit from the conductivity K and I'm getting an answer of 5774W but when I look here

http://www.chegg.com/homework-help/questions-and-answers/consider-slab-shown-figure-18-18-suppose-l-290-cm-850-cm2-material-copper-th-103-c-tc-80-c-q43179
and here
http://www.chegg.com/homework-help/questions-and-answers/consider-slab-shown-figure-18-18-suppose-l-250-cm-860-cm2-material-copper-th-124-q4982672

they are leaving the degrees in celsius. What's more, the answer in the back of my book matches these answers! How can an answer in celsius over kelvin make any sense!? Is the answer in the back of the book also wrong?!
 
Last edited:
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When you subtract the two temperatures, the difference between the two temperatures is the same in the Celsius and Kelvin scales. Thus (per degree Kelvin) and (per degree Celsius) give the same answer.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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