Question

Ao ser aquecido de 10°c para 210°c o volume de um corpo sólido aumenta 0,02 cm³. Se o volume do corpo de 10°c era 100 cm³, determine os coeficientes de dilatação térmica volumétrica, linear e superficial do material que constitui o corpo.

Answer 1

$\bullet~\text{Volume inicial:}~V_0=100~cm^3\\\\ \bullet~\text{Varia\c{c}\~ao do volume:}~\Delta V=0,02~cm^3\\\\ \bullet~\text{Varia\c{c}\~ao da temperatura:}~\Delta T=T_f-T_i=210-10=200~^oC\\\\ \bullet~\text{Coeficientes de dilata\c{c}\~ao volum\'etrica, superficial e linear:}~\gamma,~\beta~\text{e}~\alpha,\\\\\text{respectivamente, onde:}~\alpha=\dfrac{\beta}{2}=\dfrac{\gamma}{3}$

$\text{Devemos saber que:}~\Delta V=V_0\cdot\gamma\cdot\Delta T.\text{ Assim:}\\\\ \Delta V=V_0\cdot\gamma\cdot\Delta T\\\\ 0,02=100\cdot\gamma\cdot200\\\\ 0,02=20000\gamma\\\\ \gamma=\dfrac{0,02}{20000}=0,000001\\\\ \boxed{\gamma=1\times10^{-6}~^oC^{-1}}\\\\ \alpha=\dfrac{\gamma}{3}\Longrightarrow\boxed{\alpha\approx3,33\times10^{-7}~^oC^{-1}}\\\\ \beta=2\alpha\Longrightarrow\boxed{\beta\approx6,67\times10^{-7}~^oC^{-1}}$