Question

Um orficio numa panela de ferro a 20°c tem 10cm2 de area se o coeficiente de dilatação linear do ferro é de 1,2•10-5°c-1 qual sera a area desse orficio a 270°c?

Answer 1

$\texttt{Sabendo~que}~\beta=2\alpha,~\texttt{ent\~ao}~\beta=2\cdot 1,2\cdot 10^{-5}\\\\\fbox{\fbox{\beta=2,4\cdot 10^{-5} }}\\\\ \texttt{Dilata\c{c}\~ao~superficial:}~~A=A_0\cdot (1+\beta\cdot \Delta\theta)\\\\A=10\cdot (1+2,4\cdot 10^{-5}\cdot(270-20))\\A=10\cdot (1+2,4\cdot 10^{-5}\cdot 250)\\A=10\cdot (1+0,006)\\A=10\cdot1,006\\\\\fbox{\fbox{ A=10,06~cm^2 }}$


$\texttt{OBS:}\\\alpha=\texttt{coeficiente~de~dilata\c{c}\~ao~linear~(1~dimens\~ao);}\\\beta=\texttt{coeficiente~de~dilata\c{c}\~ao~superficial~(2~dimens\~oes)};\\\Delta\theta=\texttt{varia\c{c}\~ao~de~temperatura~(final~-~inicial);}$
$\texttt{A~=~\'area;}\\\texttt{Ao}\texttt{~=~\'area~inicial.}$