Question

A clock which keeps correct time at 25° C , has a pendulum made of brass. The coefficient of linear
expansion for brass is 0.000019°
C-¹. How many seconds a day will it gain if the ambient temperature
falls to 0° C?

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Answer 1

Answer:

The gain or loss in the time w.r.t. change in temperature is given by

△t=21α△θt

Now, In this question, △θ=−25oCα=1.9×10−5t=24×60×60s

So, putting values in the equation

△t=21×1.9×10−5×(−25)×24×60×60△t=−20.520s

Negative sign shows that the clock will loose 20.52s per day.

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Answer 2

As we know that,

$T = 2 \; \pi \sqrt\dfrac {l}{g}$

So, when there's a change in temperature, the value of length is said to be different. Now,

$\sf _\Delta T = \dfrac{1}{2} \alpha \Delta\theta$

Coefficient of linear expansion for brass,

$\alpha= 0.000019^{\circ}/C$

$\sf _\Delta T = \dfrac{1}{2} \alpha \Delta \theta T$

$\sf _\Delta T = 0.000019 × 25^{\circ} × 12 × 60 × 60$

$\sf \: _\Delta T = 20.52 s$