A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature `theta` along the length x of the bar from its hot end is best described by which of the following figures?

Options

A.
B.
C.
D.

Answer

C

Explanation

We know that , `(dQ)/(dt) = (KA(theta_(H) - theta))/(x)`
or `theta_(H) - theta=(dQ)/(dt)(x)/(KA) =K' x`
[where `(dQ)/(dt KA) =K'` , at steady state and `theta_(H) =` temp of hot end of metal bar]
or `theta=theta_(H) -K'x`
It is an equation of a straight line with slope - K'. Hence, graph (c) is correct.