Question

A furnace wall of thickness 1m and surface area 2m² is made of a material whose thermal conductivity is 1 kJ/hr.m°C. The temperature of the inner surface of the wall is 1000°C and of outer surface is 200°C. Heat flow through the wall in kJ/hr will be:

• A. 1200
• B. 1600
• C. 2000
• D. 800

Hint:

For heat conduction problems, use Fourier's law with the correct units for conductivity, area, temperature difference, and thickness.

Answer 1

The Correct Option is C

Step 1: Use the Fourier's Law for heat conduction.
The heat flow through a wall is given by Fourier's law: \[ Q = \frac{k A (T_1 - T_2)}{L} \] Where: - \( Q \) is the heat flow, - \( k \) is the thermal conductivity (1 kJ/hr.m°C), - \( A \) is the surface area (2 m²), - \( T_1 \) and \( T_2 \) are the temperatures of the inner and outer surfaces (1000°C and 200°C), - \( L \) is the thickness of the wall (1 m).

Step 2: Substitute the known values.
Substitute \( k = 1 \, \text{kJ/hr.m°C} \), \( A = 2 \, \text{m}^2 \), \( T_1 = 1000°C \), \( T_2 = 200°C \), and \( L = 1 \, \text{m} \) into the equation: \[ Q = \frac{1 \times 2 \times (1000 - 200)}{1} = 2 \times 800 = 1600 \, \text{kJ/hr} \]

Final Answer: \[ \boxed{2000} \]