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Physics / An Introduction to Thermal Physics 1 / Chapter 1 / Problem 60P

An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder

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A frying pan is quickly heated on the stovetop to 200°C.

Chapter 1, Problem 60P

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QUESTION:

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).

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QUESTION:

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).

ANSWER:

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 $\frac{Q}{\Delta{}t}=\ -kA\frac{dT}{dx}$ …..(1)

Here, $Q=$ amount of heat

$\Delta{}t=$ time taken for the heat to flow

$k=$ thermal conductivity

$A=$ area of cross-section of the handle

$dT=$ change in temperature

$dx=$ difference in length between the two ends

Step 1

Given, iron density $d{\ }_{iron}=7.9\ g/c{m}^{3}$

Specific heat $c=0.45\ J/g.{\ }^{0}C$

Length of the rod $L=20\ cm$

Now, mass $m=d{\ }_{iron}\times{}A\times{}L$

Let the initial room temperature be $=20{\ }^{0}$

Final temperature is $=200{\ }^{0}C$

Thermal conductivity $k=0.80\ W/cm.K$

So, the change in temperature $\Delta{}T=200{\ }^{0}C-20{\ }^{0}C=180{\ }^{0}C$

So, heat $Q=mc\Delta{}T=d{\ }_{iron}\times{}A\times{}L\times{}0.45\ J/g.{\ }^{0}C\times{}18{0}^{0}C\$

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