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A pendulum clock runs slow by 12 s per day at 40 degC and fast by 4 s per day at 20 degC. Find the temperature at which it keeps correct time and the linear expansion coefficient alpha of the pendulum shaft.

1. 55 degC; alpha = 1.85 * 10⁻² /degC
2. 25 degC; alpha = 1.85 * 10⁻⁵ /degC
3. 60 degC; alpha = 1.85 * 10⁻⁴ /degC
4. 30 degC; alpha = 1.85 * 10⁻³ /degC

Correct answer: 25 degC; alpha = 1.85 * 10⁻⁵ /degC

Solution

Using error = (1/2)*alpha*deltaT*86400 with opposite signs at 40 and 20 degC gives correct-time temperature T0 = 25 degC and alpha = 1.85 * 10⁻⁵ /degC.

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