First slide

Thermal expansion

Question

A bimetallic strip of thickness 2cm consists of zinc and silver riveted together. The approximate radius of curvature of the strip when heated through $50^{0} C$ will be $(g i v e n α_{1}, α_{2} a r e c o e f f i c i e n t s o f l i n e a r e x p a n s i o n o f z i n c = 32 \times 10^{- 6} / {}^{0}C a n d s i l v e r = 19 \times 10^{- 6} / {}^{0}C)$

Moderate

A

30.77m
B

61.54m
C

15.38m
D

7.69m

Solution

$r a d i u s o f c u r v a t u r e o f a b i m e t a l l i c s t r i p w h e n i t s t e m p e r a t u r e i s c h a n g e d t h r o u g h Δ t i s R = \frac{d}{(α_{1} ~ α_{2}) Δ t} m e t e r h e r e d i s s t r i p w i d t h = 2 \times 10^{- 2} m; α_{1}, α_{2} a r e c o e f f i c i e n t s o f l i n e a r e x p a n s i o n o f z i n c = 32 \times 10^{- 6} / {}^{0}C a n d s i l v e r = 19 \times 10^{- 6} / {}^{0}C; R = \frac{2 \times 10^{- 2}}{(32 \times 10^{- 6} - 19 \times 10^{- 6}) 50} R = \frac{2 \times 10^{- 2}}{13 \times 10^{- 6} \times 50} R = \frac{2}{65} \times 10^{3} = 30.769 R = 30.77 m$

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