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What is the rate of heat flow through a aluminum bar of area 8 cm² and length 1.5 m if there is a temperature difference of 80°C is maintained between its ends?

User Seansand
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Final answer:

To calculate the rate of heat flow through an aluminum bar with an area of 8 cm², a length of 1.5 m, and a temperature difference of 80°C, use Fourier's Law of heat conduction. Convert the area from cm² to m² and insert all the values into the equation Q = kA∆T/L, using the thermal conductivity for aluminum.

Step-by-step explanation:

The rate of heat flow through an aluminum bar given its area and temperature difference can be calculated using Fourier's Law of heat conduction, which is stated as Q = kA∆T/L, where:

  • Q is the heat flow rate,
  • k is the thermal conductivity of the material (aluminum in this case, which has a k value of 220 W/m°C),
  • A is the cross-sectional area through which heat is transferred,
  • ∆T is the temperature difference across the material,
  • L is the length of the material through which heat is being transferred.

Given the aluminum bar has an area of 8 cm² (or 8 x 10⁻´ m² since we convert to SI units), a length of 1.5 m, and a temperature difference (∆T) of 80°C, we need to insert these values into the formula and solve for Q.

To convert 8 cm² to square meters, we note that 1 cm² is equivalent to 1 x 10⁻´ m². Thus, 8 cm² is 8 x 10⁻´ m². Now, apply these values to Fourier's Law:
Q = (220 W/m°C)(8 x 10⁻´ m²)(80°C)/(1.5 m). Doing the math gives us the rate of heat conduction of the aluminum bar.

User Xavier Taylor
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