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Introductory Physics Homework Help
Derive thermal expansion of area from length
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[QUOTE="tuki, post: 6152556, member: 656961"] [B]Homework Statement:[/B] Derive thermal expansion of area from length [B]Relevant Equations:[/B] Linear thermal expansion for length: $$ \Delta l = \alpha l_0 \Delta T $$ I tried following: $$ \Delta l = \alpha l_0 \Delta T $$ $$ (\Delta l)^2 l_0 = \alpha l_0^2 \Delta T \Delta l $$ $$ \Delta A l_0 = \alpha A_0 \Delta T $$ $$ \Delta A = \frac{ \alpha A_0 \Delta T }{ l_0 } $$ If we remember that: $$ \Delta l = \alpha l_0 \Delta T $$ So we have $$ \Delta A = \frac{ \alpha A_0 \Delta T \alpha l_0 \Delta T }{ l_0 } $$ $$ \Delta A = (\alpha)^2 A_0 (\Delta T)^2 $$ However the correct solution should be; $$ \Delta A \approx (2 \alpha)A_0 \Delta T $$ Any suggestion on what's going wrong or what should i try next? [/QUOTE]
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Introductory Physics Homework Help
Derive thermal expansion of area from length
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