Heat flow question help?A brass rod with a length of 30.0 cm is placed side by side 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 coefficient of thermal conductivities of the brass and the aluminum are 100 W/m °C and 230 W/m °C respectively. The brass rod has a cross sectional area of 20.0 cm2 and the aluminum rod has a cross sectional area of 30.0 cm2. What is the heat flow from the hot temperature to the cold temperature?
542 W
54.2W
26.7 W
267 W
267 W
To calculate the heat flow from the hot temperature to the cold temperature, we can use the formula:
Q = (k * A * ΔT) / L
Where:
Q is the heat flow
k is the coefficient of thermal conductivity
A is the cross-sectional area
ΔT is the temperature difference
L is the length
For the brass rod:
k = 100 W/m °C
A = 20.0 cm^2 = 0.002 m^2 (converting cm^2 to m^2)
ΔT = 100 °C - 10.0 °C = 90 °C
L = 30.0 cm = 0.30 m (converting cm to m)
For the aluminum rod:
k = 230 W/m °C
A = 30.0 cm^2 = 0.003 m^2 (converting cm^2 to m^2)
ΔT = 100 °C - 10.0 °C = 90 °C
L = 30.0 cm = 0.30 m (converting cm to m)
Let's calculate the heat flow for each rod separately and then add them together:
For the brass rod:
Q_brass = (100 W/m °C * 0.002 m^2 * 90 °C) / 0.30 m
Q_brass = 60 W
For the aluminum rod:
Q_aluminum = (230 W/m °C * 0.003 m^2 * 90 °C) / 0.30 m
Q_aluminum = 207 W
Now, let's sum up the heat flows for both rods:
Q_total = Q_brass + Q_aluminum
Q_total = 60 W + 207 W
Q_total = 267 W
Therefore, the heat flow from the hot temperature to the cold temperature is 267 W.