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 coefficient of 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?
85.3 W
70.3 W
78.1 W
55.3 W
65.3 W
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To calculate the heat flow from the hot temperature to the cold temperature, we need to use the formula for heat conduction:
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 of the material
First, let's calculate the temperature difference (ΔT) between the hot and cold temperatures:
ΔT = T_hot - T_cold
ΔT = 100°C - 10.0°C
ΔT = 90.0°C
Next, we can calculate the heat flow for each rod using the formula above:
For the brass rod:
Q_brass = (k_brass * A * ΔT) / L
Q_brass = (100 W/m °C * 0.002 m^2 * 90.0°C) / 0.10 m
Q_brass = 20.0 W
For the aluminum rod:
Q_aluminum = (k_aluminum * A * ΔT) / L
Q_aluminum = (230 W/m °C * 0.002 m^2 * 90.0°C) / 0.30 m
Q_aluminum = 36.6 W
Finally, we can calculate the total heat flow for the system by summing up the heat flows for each rod:
Q_total = Q_brass + Q_aluminum
Q_total = 20.0 W + 36.6 W
Q_total = 56.6 W
Therefore, the heat flow from the hot temperature to the cold temperature is 56.6 W.