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?

Let Q be the temperature at a distance $x$  from hot end of bar. Let Q be is the temperature of hot end.
The heat flow rate is given by
 $\frac{dQ}{dt}=\frac{kA({\theta }_1-\theta )}{x} \Rightarrow {\theta }_1-\theta =\frac{x}{kA}\frac{dQ}{dt}\Rightarrow \theta ={\theta }_1-\frac{x}{kA}\frac{dQ}{dt}$
 
Thus, the graph of Q versus  $x$ is a straight line with a positive intercept and a negative slope.
The above equation can be graphically represented by option (a).