Fourier's Law of Heat Conduction: Calculating Temperature on the Bottom Surface of a Pan

How to calculate the temperature on the bottom surface of a pan using Fourier's Law of Heat Conduction?

An electric stove of 250W is heating a pan that has a 28cm diameter bottom with a thickness of 10mm. If the pan has a conductivity of 80W/m K and the inner surface is at 17°C, what is the temperature on the bottom surface of the pan?

Calculating the Temperature on the Bottom Surface of the Pan

To find the temperature on the bottom surface of the pan, we can use the concept of heat conduction and apply Fourier's law of heat conduction. The formula for heat conduction through a flat surface is:

Q = (k × A × ΔT) / d

Where:

Q is the heat transfer rate

k is the thermal conductivity of the material (80 W/m K)

A is the area of the surface (bottom surface of the pan)

ΔT is the temperature difference between the inner surface and the bottom surface

d is the thickness of the pan (10 mm)

Calculations

First, calculate the area of the bottom surface of the pan using the given diameter.

Next, determine the temperature difference between the bottom and inner surfaces of the pan.

Substitute the known values into the formula and solve for the temperature on the bottom surface.

Given the data of the pan's thickness, conductivity, and initial temperature of the inner surface, we can follow the steps outlined above to find the temperature on the bottom surface of the pan. By applying Fourier's Law of Heat Conduction, we can determine the final temperature accurately.

For a detailed explanation and step-by-step calculation, refer to the provided formula and numerical values in the problem statement. Understanding this process can enhance your knowledge of heat transfer and thermal conductivity in various materials.