First slide

Thermal expansion

Question

A pendulum clock is 5 seconds fast at temperature of 15 °C and 10 seconds slow at a temperature of 30 °C. Per day At what temperature does it give the correct time?

Moderate

A

18 °C
B

20 C
C

22 °C
D

25 °C

Solution

As we know
$\frac{ΔT}{T} = \frac{1}{2} αΔθ where$
$Δ θ = θ_{actual} - θ_{calibration}$
So,
$\frac{5}{10} = (\frac{T - 15}{30 - T}) \Rightarrow 30 - T = 2 T - 30$
$\Rightarrow T = 20^{\circ} C$

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