Final answer:
The heat conduction rate along the copper rod depends on the thermal conductivity, cross-sectional area, temperature difference, and length of the rod. The heat conduction rate in this case is approximately -11501.72 W.
Step-by-step explanation:
The heat conduction rate along the copper rod can be calculated using the formula:
Q = -k * A * ΔT / L
Where:
- Q is the heat conduction rate
- k is the thermal conductivity of copper
- A is the cross-sectional area of the rod
- ΔT is the temperature difference between the ends of the rod
- L is the length of the rod
In this case, the thermal conductivity of copper is approximately 401 W/m·K. The cross-sectional area of the rod can be calculated using the formula:
A = π * (d/2)^2
Where:
- d is the diameter of the rod
Substituting the given values into the formula, we have:
A = π * (2.2/2)^2 = 3.801 cm^2
ΔT = (500 - 24) °C = 476 °C
L = 62 cm
Plugging in the values, we get:
Q = -401 W/m·K * 3.801 cm^2 * 476 °C / 62 cm = -11501.72 W
The heat conduction rate along the rod is approximately -11501.72 W.