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Thermal conductivity of inner core of ra...

Thermal conductivity of inner core of radius r is K and of the outer one of radius `2r` is 2K. Find equivalent value of thermal conductivity between its two ends.

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The correct Answer is:
D
The meaning of equivalent value of thermal conductivity means, if a single material of `K_e` is used with same dimensions then value of thermal resistances should remain unchanged.

rarr
Between two ends `R_1 and R_2` are in parallel. Hence,
`1/R_1 + 1/R_2 = 1/R`
R is given by `l/(KA)`. Therefore, `1/R` will be given by `(KA)/l`. Using this in Eq. (i), we have.
` (K(pir^2))/l + ((2K[(pi)(2r)^2 - pir^2])/l) = ((K_e)(pi)(2r)^2)/l`
Solving this equation , we get
`K_e = 7/4K`.
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