Question

The temperature difference between two points on a conducting rod in thermal steady state at 2cm distance is 5°C.Find the temperature difference between two points at distance 4cm.​

Answer 1

Given: The temperature difference between two points on a conducting rod in thermal steady state at 2 cm distance is 5° C.

To find: The temperature difference between two points at distance 4 cm.​

Solution:

• In a conducting rod, the temperature gradient is always constant at all points.

        $\frac{dT}{dx} = constant$

• Here, dT is the change in the temperature and dx is the distance between the two points on the conducting rod taken into consideration.
• Hence,

        $\frac{(dT)_{1}}{(dx)_{1}} = \frac{(dT)_{2}}{(dx)_{2}}$

        $\frac{5}{2cm} = \frac{(dT_{1}) } {4cm}$

         $(dT)_{1} = 10$

• This means when the distance between two points is 4 cm from each other, the temperature difference between the two points is 10° C.

Therefore, the temperature difference is 10° C.