Question

The ends of a rod of uniform thermal conductivity are maintained at different (but 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 non-uniform cross-sectional area
• B. temperature gradient along length is 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 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 obviously flows from higher temperature to lower temperature in steady state. $\Rightarrow$ A is true.

Temperature gradient $\propto \frac{1}{\text{cross-section area}}$ in steady state. $\Rightarrow B$ is false.

Thermal current through each cross-section area is same. $\Rightarrow C$ is true.

Temperature decreases along the length of the rod from higher temperature end to lower temperature end. $\Rightarrow D$ is false.