JEE Main · 2009 · 12 Apr 2009 · Offline · Heat & Thermodynamics

Under steady state the same amount of heat flows past every cross-section of the bar each second, and Fourier's law $\frac{dQ}{dt}=kA\frac{d\theta }{dx}$ then forces the temperature gradient $\frac{d\theta }{dx}$ to be constant. A constant gradient means the temperature falls uniformly with distance, $\theta ={\theta }_H-k^{\prime }x$, so the correct description is the straight line sloping down from the hot end.