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A spherical body of radius 'b' has a con...

A spherical body of radius 'b' has a concentric cavity of radius 'a' as shown. Thermal conductivity of the material is K. Find thermal resistance between inner surface P and outer surface Q.

Text Solution

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The correct Answer is:
A, B, D
As we move from P to Q surface perpendicular to PQ is spherical and its size keeps on increasing (just like different layers of a spherical onion). So, first we will calculate thermal
resistance of one layer at a distance r from centre and thickness dr by using the formula
`R = l/(KA)`

In this formula, dimension of the layer along PQ is dr and the surface area perpendicular to PQ
is `4pir^2`
`:. dR = (dr)/(K(4pir^2))`
Now, if we integrate dR from r = a to r= b, we will get the total thermal resistance between P
and Q. Thus,
` R = int_(a)^b dR = int_(a)^b (dr)/(K(4pir^2))`
Solving this expression, we get
`R = 1/(4piK)(1/a -1/b)`.
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