Question

2 - Uma chapa de ferro de 1,2 m2 de área foi aquecida, dilatando-se. Considerando a variação de
temperatura de 10° C, qual a área final da chapa?

3- Um recipiente de ferro de 700 cm3 de volume foi aquecido, dilatando-se. Considerando a variacão de temperatura de 10°C, qual o volume final desse recipiente? ​

Answer 1

2.

$\text{Dados:}\ S_0=1.2\ \mathrm{m^2};\ \alpha=1.2\times10^{-5}^{\circ}\mathrm{C^{-1}};\ \Delta\theta=10^{\circ}C.$

$\mathrm{Coeficiente\ de\ dilata\c{c}\tilde{a}o\ superficial\ do}\ \text{ferro:}$

$\boxed{\beta\approx2\alpha}\Longrightarrow \beta\approx2(1.2\times10^{-5})\ \therefore\ \beta\approx2.4\times10^{-5}^{\circ}\mathrm{C^{-1}}$

$\mathrm{Varia\c{c}\tilde{a}o\ de\ \acute{a}}\text{rea:}$

$\boxed{\Delta S=S_0\beta\Delta\theta}\Longrightarrow \Delta S=(1.2)(2.4\times10^{-5})(10)$

$\Longrightarrow \Delta S=2.88\times10^{-4}\ \therefore\ \Delta S\approx0.000288\ m^2$

$\mathrm{\acute{A}rea}\ \text{final:}$

$\boxed{\Delta S=S-S_0}\ \therefore\ S=S_0+\Delta S$

$\Longrightarrow S=1.2+0.000288\ \therefore\ \boxed{S=1.200288\ m^2}$

3.

$\text{Dados:}\ V_0=700\ \mathrm{cm^3};\ \alpha=1.2\times10^{-5}^{\circ}\mathrm{C^{-1}};\ \Delta\theta=10^{\circ}\mathrm{C}.$

$\mathrm{Coeficiente\ de\ dilata\c{c}\tilde{a}o\ volum\acute{e}trica\ do}\ \text{ferro:}$

$\boxed{\gamma \approx3\alpha}\Longrightarrow \gamma\approx3(1.2\times10^{-5})\ \therefore\ \gamma\approx3.6\times10^{-5}^{\circ}\mathrm{C^{-1}}$

$\mathrm{Varia\c{c}\tilde{a}o\ de}\ \text{volume:}$

$\boxed{\Delta V=V_0\gamma\Delta\theta}\Longrightarrow \Delta V=(7\times10^2)(3.6\times10^{-5})(10)$

$\Longrightarrow \Delta V=25.2\times10^{-2}\ \therefore\ \Delta V\approx0.252\ \mathrm{cm^3}$

$\mathrm{Volume}\ \text{final:}$

$\boxed{\Delta V=V-V_0}\ \therefore\ V=V_0+\Delta V$

$\Longrightarrow V=700+0.252\ \therefore\ \boxed{V=700.252\ \mathrm{cm^3}}$