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

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

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