Using the equation for thermal conduction

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Thermodynamics · Thermodynamics

Problem

Using the equation for thermal conduction, calculate the following: (a) The rate of thermal energy transfer through a conductor of cross-sectional area

8\,\text{cm}^2

and thermal conductivity

200\,\text{J s}^{-1}\,{}^\circ\text{C}^{-1}\text{ m}^{-1}

if the temperature gradient across the conductor is

2.0\,{}^\circ\text{C m}^{-1}

. (b) The cross-sectional area of a conductor of length

65\,\text{cm}

and thermal conductivity

420\,\text{J s}^{-1}\,{}^\circ\text{C}^{-1}\text{ m}^{-1}

if a temperature difference of

40\,{}^\circ\text{C}

between its ends makes thermal conduction occur at a rate of

52\,\text{W}

. (c) The temperature gradient necessary to cause conduction to occur at a rate of

3.5\,\text{W}

through a conductor of cross-sectional area

25\,\text{cm}^2

and thermal conductivity

40\,\text{J s}^{-1}\,{}^\circ\text{C}^{-1}\text{ m}^{-1}

. (d) The thermal conductivity of glass if conduction occurs at a rate of

600\,\text{W}

through a window of length

2.0\,\text{m}

, height

1.6\,\text{m}

, and thickness

4.0\,\text{mm}

, when the temperatures on either side of the window are

30\,{}^\circ\text{C}

and

30.9\,{}^\circ\text{C}

Related theory

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