First slide

Thermal expansion

Question

A metal meter scale gives correct measurement at $40^{0} C$ it is generally used at a temperature of $0^{0} C$ . Find the correction to be made for every meter $(α = 10^{- 6} /^{0} C)$

Moderate

A

$4 \times 10^{- 5} m$
B

$4 \times 10^{- 5} m$ to be added
C

$4 \times 10^{- 5} m$ must be deduted
D

none of the above

Solution

$c h a n g e i n l e n g t h i s Δ l = l α Δ t l i s i n i t i a l l e n g t h o f r o d = 1 m; α i s c o e f f i c i e n t o f l i n e a r e x p a n s i o n = 10^{- 6} / {}^{0}C Δ t i s c h a n g e i n t e m p e r a t u e; d e c r e a s e d f r o m 40^{0} C t o 0^{0} C Δ l = 1 \times 10^{- 6} \times 40 Δ l = 4 \times 10^{- 5} m$
If $t_{2} < t_{1}$ so correction must be deducted.

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