A copper sheet thick and in area has one face maintained at and the other at

PHYSICS · Single correct · AP · Physics 2: Algebra-based · Thermodynamics · Thermodynamics

Problem

A copper sheet

0.50\,\text{cm}

thick and

0.020\,\text{m}^2

in area has one face maintained at

120^{\circ}\text{C}

and the other at

20^{\circ}\text{C}

. The thermal conductivity

k

of copper varies approximately linearly with temperature as follows:

k=400\,\text{W}\,\text{m}^{-1}\,\text{K}^{-1}

0^{\circ}\text{C}

k=385\,\text{W}\,\text{m}^{-1}\,\text{K}^{-1}

50^{\circ}\text{C}

, and

k=360\,\text{W}\,\text{m}^{-1}\,\text{K}^{-1}

100^{\circ}\text{C}

. Assuming

k

depends linearly on temperature, what is the approximate rate at which thermal energy is conducted through the sheet? (a)

1.1\times10^{5}\,\text{W}

(b)

3.9\times10^{5}\,\text{W}

(c)

1.5\times10^{5}\,\text{W}

(d)

7.6\times10^{4}\,\text{W}