1. Tardigrade
  2. Question
  3. Physics
  4. A clock pendulum made of invar has a period of 2 s at 20° C. If the clock is used in a climate where average temperature is 40° C, what correction (in seconds) may be necessary at the end of 10 days to the time given by clock? (α text invar =7 × 10-7 ° C -1, 1 text day =8.64 × 104 s )

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Q. A clock pendulum made of invar has a period of $2\, s$ at $20^{\circ} C$. If the clock is used in a climate where average temperature is $40^{\circ} C$, what correction (in seconds) may be necessary at the end of $10$ days to the time given by clock? $\left(\alpha_{\text {invar }}=7 \times 10^{-7 \circ} C ^{-1}, 1 \text { day }=8.64 \times 10^{4} s \right)$

Thermal Properties of Matter

Solution:

$T=2 \pi \sqrt{\frac{l}{g}} \Rightarrow \frac{\Delta T}{T}=\frac{1}{2} \frac{\Delta l}{l}=\frac{1}{2} \alpha \Delta \theta $
$\Rightarrow \Delta T=\frac{T}{2}(\alpha \Delta \theta)$
$=\left(\frac{10 \times 8.64 \times 10^{4}}{2}\right)\left(7 \times 10^{-7}\right)(20)=6\, s$