Thermal Conduction: Heat Flow Through a Bar

1 · Predict

A copper bar connects a hot body and a cold body. If you use a thicker bar (more cross-sectional area), does heat flow through it faster or slower?

• A thicker bar conducts heat faster — more area means a wider path for heat flow.
• A thicker bar conducts heat slower.
• Bar thickness doesn't affect the conduction rate.

2 · Set Up

1. Open the conduction-bar preset and press Reset. A copper bar (k = 401 W/(m·K), length 0.1 m) connects a 450 K body to a 300 K body.
2. Enable the heat-flow-rate readout on the conductor.
3. Set the bar's cross-sectional area for each trial and record the heat-flow rate.

3 · Collect Data

Plot heat-flow rate Q̇ (y-axis) against cross-sectional area A (x-axis) for your three trials. Is the line straight through the origin?

4 · Analyze

1. For one trial, compute Q̇ = kAΔT/L using k = 401 W/(m·K), ΔT = 150 K, L = 0.1 m. Compare to the table.
2. Explain, using Fourier's law, why doubling the bar's cross-sectional area doubles the rate of heat flow at fixed temperature difference and length.

5 · Extend

1. A material with low thermal conductivity (like glass, k ≈ 0.8 W/(m·K)) conducts heat far more slowly than copper (k = 401 W/(m·K)) for the same area and length. Explain why house insulation uses low-k materials.
2. This experiment varies area, but the formula also has length L in the denominator. Would doubling the bar's length double or halve the heat-flow rate? Explain why a longer path resists heat flow more.

The Physics Behind This Experiment

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