Question

A metal bar of length l is well lagged with some non-conducting material to prevent losses of heat from its surface and the two ends are maintained at steady temperature ${\theta }_1$ and ${\theta }_2$ with ${\theta }_1>{\theta }_2$, then in the steady state the temperature $\theta$ of a section of the bar at distance X from the hot end varies as shown in the graph

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (B)

2

The body is in steady state, hence the temperature gradient is a constant.
Since the temperature is decreasing with distance, the temperature gradient is negative.
i.e.
$\frac{d\theta }{dx}=-c$
$\theta +cx=b$ gives us the equation of the temperature versus distance. Which matches with graph 2