A brass rod with a length of 20.0 cm is placed side by side with an aluminum rod with a length of 20.0 cm, and this system is placed between a hot temperature of 150 °C and a cold temperature of −10.0 °C. The thermal conductivities of the brass and the aluminum are 100 W/m °C and 230 W/m °C, respectively. The rods have the same cross-sectional area of 20.0 cm². What is the rate of heat flow from the hot temperature to the cold temperature?

Question

Quizplus · Accepted Answer

The rate of heat flow can be calculated using the formula:

Q/t = kA(deltaT)/L

where Q/t is the rate of heat flow, k is the thermal conductivity, A is the cross-sectional area, delta T is the difference in temperature, and L is the length of the rod.

For brass:
Q/t = (100 W/m °C)(0.002 mS1U1P12S1S1P0S1S1P12S1S1P0)(150 °C - (-10.0 °C))/(0.20 m) = 415 W

For aluminum:
Q/t = (230 W/m °C)(0.002 mS1U1P12S1S1P0S1S1P12S1S1P0)(150 °C - (-10.0 °C))/(0.20 m) = 956 W

Since the rods are in thermal contact with each other, the rate of heat flow through both rods together will be the same.

Therefore, the total rate of heat flow is:

Q/t = 2(415 W + 956 W) = 2,742 W

Rounding to one significant figure, the answer is 528 W. Therefore, the best choice is B.

A Brass Rod with a Length of 20