Question

A pendulum clock loses 12 s a day if the temperature is 40°C and gains 4 s in a day if the temperature is 20°C.

Answer 1

Time loss or gain is given by

Δt=(ΔTT)t=12αθ.t

12=12α(40−θ0)×Id ----(1)

4=12α(θ0−20)×Id ----(2)

(1)(2) gives

3=(40−θ0)(θ0−20)

Solving θ0=25∘C and putting in (2)

α=85×29×60×60

=1.85×10−5/∘C