First slide

Thermal expansion

Question

The length of each rail is 10m. The linear expansion of steel is $0.000012 /^{0} C$ and the range of variation of temperature at the given place is $15^{0} C$ . So the gap to be provided between the rail is

Moderate

A

$0.0018 m$
B

$0.0012 m$
C

$0.0022 m$
D

$0.02 m$

Solution

$c h a n g e i n l e n g t h d u e t o v a r i a t i o n i n t e m p e r a t u r e i s Δ l = l α Δ t h e r e l i s i n i t i a l l e n g t h = 10 m; α i s c o e f f i c i e n t o f l i n e a r e x p a n s i o n = 12 \times 10^{- 6} / {}^{0}C Δ t i s c h a n g e i n t e m p e r a t u r e = 15^{0} C Δ l = 10 \times 12 \times 10^{- 6} \times 15 Δ l = 180 \times 10^{- 5} = 18 \times 10^{- 4} Δ l = 0.0018 m = g a p b e t w e e n 2 r a i l s t o b e m a i n t a i n e d$

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