Question

The heat flows through a rod of length $50\, cm$ and area of cross-section $5\, cm ^{2}$. Its ends are respectively at $25^{\circ} C$ and $125^{\circ} C$. The coefficient of thermal conductivity of the material rod is $0.092\, kcal / m ^{\circ} C$. The temperature gradient of the rod is

• A. $2^{\circ} C / cm$
• B. $2^{\circ} C / m$
• C. $20^{\circ} C / cm$
• D. $20^{\circ} C / m$

Answer 1

Answer: (A)

Temperature gradient of the rod
$\frac{\Delta \theta}{\Delta x}=\frac{\theta_{2}-\theta_{1}}{l}$
$\therefore \frac{\Delta \theta}{\Delta x} =\frac{125-25}{50}$
$=\frac{100}{50}=2^{\circ} C / cm$