Physics·Heat·Gas/Principles and Exploration
Heat conduction in a rod — principles and investigation
The temperature distribution of the rod between the hot and cold sides changes over time. By changing the material, length, and temperature at both ends, we compare the heat transfer process and the state after sufficient time has passed. Read separately the speed at which heat is transferred and the shape of the final temperature distribution.
How does it work?
Heat spreads through temperature differences, and after enough time, it approaches a linear distribution.
∂T/∂t = α ∂²T/∂x² · r = αΔt/Δx² ≤ 0.5
Try this investigation
- The temperature reservoir at both ends remains constant. The inside starts at 20 °C, and the colored bands show how the heat spreads. Compresses 1200 s of real time into 10 s of screen time.
- Press the standard conditions button, run it, and record each measurement value.
- Materials change the speed at which heat spreads. At constant end temperatures, the final linear distribution is independent of the material. Longer rods are less likely to reach equilibrium even in 1200 s.
Interpreting your results
As the thermal diffusivity increases, what time does it take to reach equilibrium at the same length?
The characteristic time is proportional to L²/α, so the greater the thermal diffusivity, the shorter it becomes.
Assumptions and limitations
Assume a uniform one-dimensional bar and a constant thermal diffusivity. There is no side heat loss or contact resistance. Calculate FTCS with 31 grids and maintain r≤0.45 with internal time partitioning. The temperature at both ends is fixed.