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Q. A pendulum clock is $5$ seconds fast at temperature of $15^{\circ} C$ and $10$ seconds slow at a temperature of $30^{\circ} C$. At what temperature does it give the correct time? (take time interval $=24$ hours)

Thermal Properties of Matter

Solution:

$\Delta t =\frac{1}{2} \alpha \Delta T \times t $
$\therefore 5=\frac{1}{2} \alpha( T -15) \times 86400$
and $10=\frac{1}{2} \alpha(30- T ) \times 86400$