The area of cross-section of rod is given by `A= A_(0) (1+alphax)` where `A_(0)` & `alpha` are constant and x is the distance from one end. If the thermal conductivity of the material is `K`. What is the thermal resistancy of the rod if its length is `l_(0)`?

Options

A. `KA_(0)alphaln(1+alphal_(0))`
B. `(1)/(KA_(0)alpha)ln(1+alphal_(0))`
C. `(alpha)/(KA_(0)alpha)ln(1+alphal_(0))`
D. `(KA_(0))/(alpha)ln(1+alphal_(0))`

Answer

B

Explanation

`dR_(H) = (dx)/(KA) = (dx)/(KA_(0)(1+alphax)`
`R_(H) = intdR_(H) = underset(0)overset(t)int (dx)/(KA_(0)(1+alphax)) = (1)/(KA_(0)) ((ln(1+alphax))/(alpha))_(0)^(t)`
=` (1)/(KA_(0)alpha) ln(1+alphal_(0))`

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