Calorimeter Homework: Clock Period & Temperature Change

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SUMMARY

The discussion centers on a homework problem involving a pendulum clock designed to operate at 20.0°C but functioning at −80.0°C. The key equations used include the coefficient of linear expansion of aluminum (2.31×10−5 1/C°) and the formulas for heat transfer (Q = cmΔT) and linear expansion (ΔL = LiαΔT). The primary questions address whether the clock will run fast or slow and how many periods it will take before the clock is off by 1.00 second. The solution requires calculating the change in length of the pendulum due to temperature variation.

PREREQUISITES
  • Understanding of pendulum mechanics and period calculation
  • Familiarity with the coefficient of linear expansion
  • Knowledge of heat transfer equations
  • Basic algebra for solving equations
NEXT STEPS
  • Calculate the effect of temperature on pendulum length using ΔL = LiαΔT
  • Determine the period of a pendulum using the formula T = 2π√(L/g)
  • Explore the implications of temperature changes on timekeeping accuracy
  • Research the properties of aluminum and its thermal expansion characteristics
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and thermodynamics, as well as educators looking for practical examples of pendulum behavior under varying temperature conditions.

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Homework Statement



A clock is designed with a simple pendulum, consisting of a mass at the end of an aluminum rod, whose period is supposed to be equal to one second. The clock is designed to keep accurate time at 20.0°C, but is operated at a constant temperature of −80.0°C. (a) Will the clock run fast or slow? Explain. (b) How many periods will the pendulum go through before the clock is off by 1.00 s? (The coefficient of linear expansion of aluminum is 2.31×10−5 1/C°.)

Homework Equations


Q = cmΔT
Qw + Qo = 0
ΔL = LiαΔT



The Attempt at a Solution


i tried several time using those equation above, but it didnot give the right answer, please help or give me hints.thank
 
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