Sample Solution from
An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Chapter 1.7
Problem 56P
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Textbook Problem

Calculate the rate of heat conduction through a layer of still air that is 1 mm thick, with an area of 1   m 2 , for a temperature difference of 20 ° C .

Expert Solution
To determine

The rate of heat conduction through a layer of still air.

Answer

  QΔt=520watts

Explanation of Solution

Given:

Thickness of air, Δx=1mm=0.001m

Area of the layer of air, A=1m2

Temperature difference, ΔT=20°C

Thermal conductivity of air, kt=0.026J.s-1m-1.K-1

Formula Used:

Rate of heat conduction:

  QΔt=ktAΔTΔx

Where Q is the amount of heat, and Δt is the time interval

Calculation:

The rate of heat conduction through a layer of still air is

  QΔt=ktAΔTΔx=0.026×1×200.001=520watts

Conclusion:

  QΔt=520watts

The negative sign indicates that heat flows down the temperature gradient.

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