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

Practice Questions

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)

200 W
400 W
600 W
800 W

Questions & Step-by-Step Solutions

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.

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

Practice Questions

Questions & Step-by-Step Solutions

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