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A copper rod is 0.825 m long with a rectangular cross-section of dimensions 0.0539 m by 0.0761 m. The ends of the rod are held at temperatures of 56.3 °C and 99.1 °C, while the rod is otherwise insulated from its environment.

Find the heat current (the amount of heat that flows per unit time) through the rod. The thermal conductivity of copper is 385 W/(m·K).

Answer :

Final answer:

The rate of heat current through the copper rod can be calculated using the formula for heat conduction, factoring in copper's thermal conductivity, the cross-sectional area of the rod, temperatures at both ends of the rod, and the length of the rod.

Explanation:

To calculate the heat current, you have to use the formula for heat conduction which is Q = k*A*(Th-Tc)/d, where:

  • 'k' is the thermal conductivity of the material,
  • 'A' is the cross-sectional area of the material,
  • 'Th' and 'Tc' are the hot and cold temperatures respectively,
  • 'd' is the length of the material.

In this case, the thermal conductivity of copper 'k' is 385 W/(m·K), the cross-sectional area 'A' can be calculated by multiplying the cross-section dimensions (0.0539 m * 0.0761 m), the temperature difference 'Th-Tc' is the difference between the end temperatures (99.1 °C - 56.3 °C), and the length 'd' is 0.825 m. Plug these values into the formula and calculate the heat current.

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