Question

Um recipiente de vidro (ᵦ= 0,000027 / °C) contém 800 centímetros cúbicos de álcool (ᵦ= 0,0011 /°C) que ocupa todo o recipiente a -10°C. Quando aquecermos o recipiente e o álcool a uma temperatura de 70°C, o volume de álcool que transbordará em centímetros cúbicos

Answer 1

$Calculando \ \gamma_{ap}: \\\\ \beta_R=0,000027 = 2,7.10^{-5} \ ^oC^{-1} \\ \gamma_R= \frac{3. \beta_R}{2}= \frac{3.2,7.10^{-5}}{2}= \frac{8,1.10^{-5}}{2}=4,05.10^{-5} \ ^oC^{-1} \\\\ \beta_L=0,0011=1,1.10^{-3} \ ^oC^{-1} \\ \gamma_L= \frac{3. \beta_L}{2}= \frac{3.1,1.10^{-3}}{2}= \frac{3,3.10^{-3}}{2}=1,65.10^{-3} \ ^oC^{-1} \\\\ \gamma_{ap}= \gamma_L- \gamma_R \\ \gamma_{ap}=1,65.10^{-3}-4,05.10^{-5} \\ \gamma_{ap}=165.10^{-5}-4,05.10^{-5} \\ \gamma_{ap}=160,95.10^{-5}=1,6095.10^{-3}$

$Calculando \ \Delta V: \\\\ \Delta V=V_0. \gamma_{ap}.\Delta T \\ \Delta V=8.10^2.1,6095.10^{-3}.80 \\ \Delta V=12,876.10^{-1}.8.10^1\\ \Delta V= 103,008 \ cm^3$