Tru Physics

Problem 1.8 (Schroeder’s Intro to Thermal Physics)

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Problem 1.8

For a solid, we also define the linear thermal expansion coefficient, \alpha, as the fractional increase in length per degree:

\alpha \equiv \dfrac{\Delta L / L}{\Delta T}.

(a) For steel, \alpha is 1.1 \times 10^{-5} \text{K}^{-1}. Estimate the total variation in length of a 1-km steel bridge between a cold winter night and a hot summer day.
(b) The dial thermometer in Figure 1.2 uses a coiled metal strip made of two different metals laminated together. Explain how this works.
(c) Prove that the volume thermal expansion coecient of a solid is equal to the sum of its linear expansion coecients in the three directions: \beta = \alpha_x + \alpha_y + \alpha_z. (So for an isotropic solid, which expands the same in all directions, \beta = 2 \alpha.)

Solution:

Problem 1.8 (Schroeder's Intro to Thermal Physics) 1 of 2
Problem 1.8 (Schroeder's Intro to Thermal Physics) 2 of 2

Problem 1.8 Solution (Download) 1 of 2

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