A thin rod, length `L_(0)` at `0^(@)C` and coefficient of linear expansion `alpha` has its two ends mintained at temperatures `theta_(1)` and `theta_(2)` respectively Find its new length .

A thin rod, length `L_(0)` at `0^(@)C` and coefficient of linear expan

1.	A thin rod, length `L_(0)` at `0^(@)C` and coefficient of linear expansion `alpha` has its two ends mintained at temperatures `theta_(1)` and `theta_(2)` respectively Find its new length .
Answer» Consider the temperature of the rod varies linearly from one end to other end. Let `theta` be the temperature of the rod at the mid point of rod. At steady state `(dQ)/(dt) = (KA(theta_1 -theta))/(L_0//2) = (KA(theta- theta_2))/(L_0//2) or theta_1 - theta = theta - theta_2 or theta = (theta_1 + theta_2)/(2)` Using, `L = L_0 (1 +alpha theta),` We have `L = L_0[1 + alpha((theta_1 + theta_2)/(2))]`

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A thin rod, length `L_(0)` at `0^(@)C` and coefficient of linear expansion `alpha` has its two ends mintained at temperatures `theta_(1)` and `theta_(2)` respectively Find its new length .

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