A brass key ($\alpha$ = 19 * 10^-6 $\circ$ C^-1,$\beta$ = 57 * 10^-6 $\circ$ C^-1)is heated from 20.0 $\circ$ C up to 180.0 $\circ$ C.If the initial length is 6.00 cm,what is the final length? A)6.00 cm B)6.02 cm C)6.05 cm D)6.0547 cm E)6.30 cm

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Quizplus · Accepted Answer

The linear expansion formula is used: $ \Delta L = \alpha \times L_0 \times \Delta T $. Here, $ \alpha = 19 \times 10^{-6} $, $ L_0 = 6.00 $ cm, and $ \Delta T = 180.0 - 20.0 = 160.0 $°C. Calculating gives $ \Delta L = 19 \times 10^{-6} \times 6.00 \times 160.0 = 0.01824 $ cm. The final length is $ 6.00 + 0.01824 \approx 6.02 $ cm.

A Brass Key α\alphaα = 19 * 10-6 ∘\circ∘ C-1 β\betaβ

A Brass Key $\alpha$ = 19 * 10^-6 ^$\circ$C^-1 $\beta$