Problem

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

8 \text{ cm}^2

and conductivity

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

if the temperature gradient across the conductor is

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

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

65 \text{ cm}

and conductivity

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

if the difference in temperature between its ends of

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

makes thermal conduction occur at a rate of

52 \text{ W}

c. 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} \text{ } ^\circ\text{C}^{-1} \text{ m}^{-1}

d. 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 \text{ } ^\circ\text{C}

and

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

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