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
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?
Solution
To solve this problem, we need to use the formula for the rate of heat flow (Q/t), which is given by:
Q/t = kA(Th - Tc)/L
where:
- Q/t is the rate of heat flow,
- k is the thermal conductivity,
- A is the cross-sectional area,
- Th is the hot temperature,
- Tc is the cold temperature, and
- L is the length of the rod.
First, we need to convert the lengths and areas from cm to m, because the thermal conductivity is given in W/m °C. So, the length of the rods is 0.2 m and the cross-sectional area is 0.002 m².
Next, we calculate the rate of heat flow for each rod separately.
For the brass rod:
Q/t = 100 W/m °C * 0.002 m² * (150 °C - (-10 °C)) / 0.2 m = 160 W
For the aluminum rod:
Q/t = 230 W/m °C * 0.002 m² * (150 °C - (-10 °C)) / 0.2 m = 368 W
Finally, since the rods are placed side by side, the total rate of heat flow from the hot temperature to the cold temperature is the sum of the rates for each rod, which is 160 W + 368 W = 528 W.
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