A brass rod with a length of 10.0 cm is placed end to end with an aluminum rod with a length of 30.0 cm, and this system is placed between a hot temperature of 100 °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 heat flow from the hot temperature to the cold temperature?

Question

Quizplus · Accepted Answer

To solve the problem, we need to use the formula for heat flow:

Q = (kA/L)ΔT

where Q is the heat flow, k is the thermal conductivity, A is the cross-sectional area, L is the length, and ΔT is the temperature difference between the hot and cold ends.

Let's first find the heat flow for the brass rod:

Q1 = (100 W/m °C)(0.0020 m²)/(0.10 m)(100 °C - 10.0 °C) 
Q1 = 800 W

Now let's find the heat flow for the aluminum rod:

Q2 = (230 W/m °C)(0.0020 m²)/(0.30 m)(100 °C - 10.0 °C) 
Q2 = 518.3 W

The total heat flow is the sum of the two heat flows:

Qtotal = Q1 + Q2 
Qtotal = 800 W + 518.3 W 
Qtotal = 1318.3 W

However, we need to convert this to watts per meter. Since the total length of the rod system is 40.0 cm, or 0.40 m, the heat flow per meter is:

Qtotal,m = Qtotal/(0.40 m) 
Qtotal,m = 1318.3 W/0.40 m 
Qtotal,m = 3295.8 W/m

Finally, we can convert this to the nearest tenth of a watt using one significant figure:

Qtotal,rounded = 3.3 × 10³ W/m ≈ 78.1 W

Therefore, the answer is D: 78.1 W.

A Brass Rod with a Length of 10