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)
Practice Questions
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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)
200 W
400 W
600 W
800 W
Using Fourier's law: Q/t = kA(ΔT/L) = 200 W/m°C * 0.0001 m² * (100°C/1 m) = 200 W.
Questions & Step-by-step Solutions
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Q
Q: 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)
Solution: Using Fourier's law: Q/t = kA(ΔT/L) = 200 W/m°C * 0.0001 m² * (100°C/1 m) = 200 W.
Steps: 7
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.
