Question

The ends of a rod of uniform thermal conductivity are maintained at different (constant) temperatures. After the steady state is achieved:

• A. Heat flows in the rod from high temperature to low temperature even if the rod has a non-uniform cross sectional area.
• B. Temperature gradient along the length is the same even if the rod has non-uniform cross-sectional area.
• C. Heat current is same even if the rod has non-uniform cross-sectional area.
• D. If the rod has uniform cross-sectional area, the temperature is the same at all points of the rod.

Answer 1

Answer: (A), (C)

Heat current is same even if the rod has non-uniform cross-sectional area.

Heat always flows from higher temperature to lower temperature. $\Rightarrow \left(a\right)$ is true.

From $\frac{dQ}{dt}=\frac{kAdT}{dx}$,
Temperature gradient $\frac{dT}{dx}\propto \frac{1}{A}$ in steady state.
$\Rightarrow \left(b\right)$ is false.

Thermal current through each cross-section is the same.
$\Rightarrow \left(c\right)$ is true.

Temperature decreases along the length of the rod from higher temperature end to lower temperature end.
$\Rightarrow \left(d\right)$ is false.