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
To calculate the heat flow, we can use the formula:
Q = ((k1 * A1) / L1) * (T2 - T1)
Where:
Q = Heat flow
k1 = Thermal conductivity of material 1 (brass in this case)
A1 = Cross-sectional area of material 1 (brass rod)
L1 = Length of material 1 (brass rod)
T2 = Cold temperature
T1 = Hot temperature
Let's calculate the heat flow step by step:
1. Convert the lengths to meters:
Length of brass rod (L1) = 30.0 cm = 0.30 m
Length of aluminum rod (L2) = 30.0 cm = 0.30 m
2. Convert the areas to square meters:
Cross-sectional area of brass rod (A1) = 20.0 cm² = 0.0020 m²
Cross-sectional area of aluminum rod (A2) = 30.0 cm² = 0.0030 m²
3. Calculate the heat flow for each rod:
Q1 = ((k1 * A1) / L1) * (T2 - T1) (for brass)
Q2 = ((k2 * A2) / L2) * (T2 - T1) (for aluminum)
Given values:
k1 = 100 W/m °C (thermal conductivity of brass)
k2 = 230 W/m °C (thermal conductivity of aluminum)
T1 = 100 °C (hot temperature)
T2 = 10.0 °C (cold temperature)
Let's calculate Q1 for the brass rod:
Q1 = ((100 W/m °C * 0.0020 m²) / 0.30 m) * (10.0 °C - 100 °C)
= (0.2 W/°C * 0.00667 m) * (-90.0 °C)
= -0.00134 W/m * (-90.0 °C)
= 0.1206 W
Let's calculate Q2 for the aluminum rod:
Q2 = ((230 W/m °C * 0.0030 m²) / 0.30 m) * (10.0 °C - 100 °C)
= (0.690 W/°C * 0.01 m) * (-90.0 °C)
= -0.0069 W/m * (-90.0 °C)
= 0.621 W
4. Calculate the total heat flow:
Total heat flow (Q) = Q1 + Q2
= 0.1206 W + 0.621 W
= 0.7416 W
Therefore, the heat flow from the hot temperature to the cold temperature is approximately 0.742 W.
None of the given answer choices (542 W, 54.2 W, 26.7 W, 267 W) matches the calculated heat flow.