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A metal rod of length 1 m and cross-sectional area 1 cm² is heated at one end. I

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Question: A metal rod of length 1 m and cross-sectional area 1 cm² is heated at one end. If the temperature difference between the ends is 100°C, what is the rate of heat transfer through the rod? (Thermal conductivity of the metal = 200 W/m°C)

Options:

  1. 200 W
  2. 400 W
  3. 600 W
  4. 800 W

Correct Answer: 200 W

Solution: 

Using Fourier\'s law: Q/t = kA(ΔT/L) = 200 W/m°C * 0.0001 m² * (100°C/1 m) = 200 W.

A metal rod of length 1 m and cross-sectional area 1 cm² is heated at one end. I

Practice Questions

Q1
A metal rod of length 1 m and cross-sectional area 1 cm² is heated at one end. If the temperature difference between the ends is 100°C, what is the rate of heat transfer through the rod? (Thermal conductivity of the metal = 200 W/m°C)
  1. 200 W
  2. 400 W
  3. 600 W
  4. 800 W

Questions & Step-by-Step Solutions

A metal rod of length 1 m and cross-sectional area 1 cm² is heated at one end. If the temperature difference between the ends is 100°C, what is the rate of heat transfer through the rod? (Thermal conductivity of the metal = 200 W/m°C)
  • Step 1: Identify the given values from the problem. We have a metal rod with a length of 1 meter, a cross-sectional area of 1 cm², a temperature difference of 100°C, and a thermal conductivity of 200 W/m°C.
  • Step 2: Convert the cross-sectional area from cm² to m². Since 1 cm² = 0.0001 m², the area A = 0.0001 m².
  • Step 3: Write down Fourier's law of heat conduction, which states that the rate of heat transfer (Q/t) is equal to the thermal conductivity (k) multiplied by the area (A) and the temperature difference (ΔT) divided by the length (L). The formula is Q/t = k * A * (ΔT / L).
  • Step 4: Substitute the known values into the formula. We have k = 200 W/m°C, A = 0.0001 m², ΔT = 100°C, and L = 1 m.
  • Step 5: Calculate the rate of heat transfer. Plugging in the values: Q/t = 200 W/m°C * 0.0001 m² * (100°C / 1 m).
  • Step 6: Perform the multiplication: Q/t = 200 * 0.0001 * 100 = 200 W.
  • Step 7: Conclude that the rate of heat transfer through the rod is 200 Watts.
  • Fourier's Law of Heat Conduction – This law states that the rate of heat transfer through a material is proportional to the temperature difference across it, the area through which heat is being transferred, and the material's thermal conductivity.
  • Thermal Conductivity – A property of a material that indicates its ability to conduct heat, measured in watts per meter per degree Celsius (W/m°C).
  • Heat Transfer Rate Calculation – The process of calculating the rate of heat transfer using the formula Q/t = kA(ΔT/L), where Q/t is the heat transfer rate, k is thermal conductivity, A is the cross-sectional area, ΔT is the temperature difference, and L is the length of the rod.
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