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Answer :
Answer:
Heat current = 71.926J/sec
Explanation:
Detailed explanation and calculation is shown in the image below
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Rewritten by : Jeany
Final answer:
The heat current through the copper rod is calculated using Fourier's Law of Heat Conduction. With a thermal conductivity of 385 W/m·K, cross-sectional area of 0.00413125 m², and a temperature difference of 39.4 K across a length of 0.871 m, the heat current is approximately 18.46 Watts.
Explanation:
For calculating heat current through a copper rod we can use Fourier's Law of Heat Conduction .It states that the time rate of heat flow Q through a material is proportional to the negative gradient in the temperature and to the area through which the heat flows. The formula is:
Q = -k * A * (dT/dx)
Where:
Q is the heat current (Watts, W)
k is the thermal conductivity of the material (W/m·K)
A is the cross-sectional area (m²)
dT is the temperature difference between the two ends (K)
dx is the length of the material (m)
The given parameters are:
Length of the copper rod (dx) = 0.871 m
Cross-sectional area (A) = 0.0533 m * 0.0775 m
Temperature difference (dT) = 97.7 ℃ - 58.3 ℃
Thermal conductivity of copper (k) = 385 W/m·K
First, we need to convert the temperature difference to Kelvin. Since the difference in Celsius is the same as in Kelvin:
dT = 97.7 - 58.3 = 39.4 K
Next, we calculate the cross-sectional area:
A = 0.0533 m * 0.0775 m = 0.00413125 m²
Then we can calculate the heat current:
Q = -385 W/m·K * 0.00413125 m² * 39.4 K / 0.871 m
Q = -18.46 W (approx., the negative sign indicates the direction of heat flow from hot to cold)
The heat current through the copper rod is therefore approximately 18.46 Watts.
