Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

We know, in steady state, heat flow rate is given by,

$\frac{dQ}{dt}=\frac{KA(T_0-T)}{\text{x}}$

$\Rightarrow (T_0-T)=\frac{x}{KA}\frac{dQ}{dt}$

$\Rightarrow T=T_0-\frac{x}{KA}\frac{dQ}{dt}$

Where is $T_1$ is the temperature of hot end and $T$ is the temperature at a distance $x$ from the hot end.

In a steady state, the rate of heat flow is constant, so the above equation can be graphically represented by

Hence, option $\left(D\right)$ is correct.