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Two thin conectric shells made of copper...

Two thin conectric shells made of copper with radius `r_(1)` and `r_(2) (r_(2) gt r_(1))` have a material of thermal conductivity `K` filled between them. The inner and outer spheres are maintained at temperature `T_(H)` and `T_(C)` respectively by keeping a heater of power `P` at the centre of the two sphers. Find the value of `P`.

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AI Generated Solution

To find the power \( P \) supplied by the heater at the center of two concentric copper shells with radii \( r_1 \) and \( r_2 \) (where \( r_2 > r_1 \)), we can follow these steps: ### Step 1: Understand the Setup We have two concentric shells with an inner radius \( r_1 \) and an outer radius \( r_2 \). The inner shell is maintained at a temperature \( T_H \) and the outer shell at \( T_C \). The heater at the center provides a power \( P \) to maintain these temperatures. ### Step 2: Define the Heat Flow The heat flows from the inner shell (higher temperature \( T_H \)) to the outer shell (lower temperature \( T_C \)). The rate of heat transfer can be expressed in terms of thermal current \( I \), which is equivalent to the power \( P \) supplied by the heater. ...
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