Problem 60P

A frying pan is quickly heated on the stovetop to 200°C. It has an iron handle that is 20 cm long. Estimate how much time should pass before the end of the handle is too hot to grab with your bare hand. (Hint: The cross sectional area of the handle doesn’t matter. The density of iron is about 7.9 g/cm3 and its specific heat is 0.45 J/g∙° C).

Solution 60P

To solve this question, we shall have to consider the Fourier heat conduction law. The mathematical equation for Fourier heat conduction law is written as …..(1)

Here, amount of heat

time taken for the heat to flow

thermal conductivity

area of cross-section of the handle

change in temperature

difference in length between the two ends

Step 1

Given, iron density

Specific heat

Length of the rod

Now, mass

Let the initial room temperature be

Final temperature is

Thermal conductivity

So, the change in temperature

So, heat