First slide

Thermal expansion

Question

A clock with a metal pendulum beating seconds keeps correct time at 0°C. If it loses 12.5 s a day at 25°C, the coefficient of linear expansion of metal pendulum is

Moderate

A

$\frac{1}{86400} / {}^{\circ}C$
B

$\frac{1}{43200} / {}^{\circ}C$
C

$\frac{1}{14400} / {}^{\circ}C$
D

$\frac{1}{28800} / {}^{\circ}C$

Solution

Number of seconds lost in a day, $Δ t = \frac{1}{2} α Δ θ \times 86400$
The coefficient of linear expansion of metal pendulum,
$α = \frac{2 Δ t}{Δ θ \times 86400} = \frac{2 \times 12.5}{25 \times 86400}$
$\Rightarrow$ $α = \frac{1}{86400} / {}^{\circ}C$

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