The two ends of a rod of length `L` and a uniform cross-sectional area `A` are kept at two temperature `T_(1)` and `T_(2)` `(T_(1) gt T_(2))`. The rate of heat transfer. `(dQ)/(dt)`, through the rod in a steady state is given by

Options

A. `(dQ)/(dt)=(KL(T_(1)-T_(2)))/A`
B. `(dQ)/(dt)=(K(T_(1)-T_(2)))/(LA)`
C. `(dQ)/(dt)=KLA(T_(1)-T_(2))`
D. `(dQ)/(dt)=(KA(T_(1)-T_(2)))/L`

Answer

D

Explanation

For a rod of length L and area of cross-section A whose faces are maintained at temperature `T_(1)` and `T_(2)` respectively.
Then in steady state the rate of heat flowing from one face to the other face in time t is given by
`(dQ)/(dt)=(KA(T_(1)-T_(2)))/L`
The curved surface of rod is kept insulated from surrounding to avoid leakage of heat