Thermal Pendulum Clock. One problem that early pendulum clocks faced was inconsistencies due to thermal expansion. Consider a long pendulum clock of thermal expansion coefficient a = 30 x 10-K-. Its length is perfectly set such that it makes half a period in 1s at 15 C. A change in temperature, however, causes this length to change by a factor of eAT, Suppose this pendulum elock is kept at 40°C for exactly 1 week. After exactly 1 week, how many seconds earlier (positive) or later (negative) would the clock's midnight be compared to the true midnight?

Physics for Scientists and Engineers with Modern Physics
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Author:Raymond A. Serway, John W. Jewett
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Chapter18: Temperature
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Thermal Pendulum Clock.
One problem that early pendulum clocks faced was
inconsistencies due to thermal expansion. Consider a long pendulum clock of thermal expansion coefficient
a = 30 x 10- K-1. Its length is perfectly set such that it makes half a period in 1s at 15 °C. A change in
temperature, however, causes this length to change by a factor of eAT. Suppose this pendulum clock is kept
at 40 °C for exactly 1 week. After exactly 1 week, how many seconds earlier (positive) or later (negative)
would the clock's midnight be compared to the true midnight?
Transcribed Image Text:Thermal Pendulum Clock. One problem that early pendulum clocks faced was inconsistencies due to thermal expansion. Consider a long pendulum clock of thermal expansion coefficient a = 30 x 10- K-1. Its length is perfectly set such that it makes half a period in 1s at 15 °C. A change in temperature, however, causes this length to change by a factor of eAT. Suppose this pendulum clock is kept at 40 °C for exactly 1 week. After exactly 1 week, how many seconds earlier (positive) or later (negative) would the clock's midnight be compared to the true midnight?
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