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Thermal Expansion

A bimetallic ...

Question

A bimetallic strip of steel and brass of length 10 cm, initially at $15^{o} C$ , is heated to $45^{o} C$ . What is the difference in length between the two substances after they have been heated? The coefficient of linear expansion for steel is $1.2 \times 10^{5} / C^{o}$ , and the coefficient of linear expansion for brass is $1.9 \times 10^{5} / C^{o}$ .

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Solution

The length of steel strip after heating= $L_{0_{s t e e l}} α_{s t e e l} Δ T$
The length of brass strip after heating= $L_{0_{b r a s s}} α_{b r a s s} Δ T$
Hence the difference in length of the two= $(L_{0}) (α_{b r a s s} - α_{s t e e l}) Δ T$
$= 10 c m \times (0.7 \times 10^{- 5} /^{\circ} C) \times 30^{\circ} C$
$= 2.1 \times 10^{- 3} c m$

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