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2 months ago

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1.- Un balín de acero a 20 C tiene un volumen de 0.004 m3. ¿Cuál es la dilatación que sufre cuando su temperatura aumenta a 50 C

?

1 answer:

Softa [3K]2 months ago

0 0

Answer:

$\Delta V = 1.440\times 10^{-6}\,m^{3}$

Explanation:

El cálculo del coeficiente de expansión volumétrica se realiza a partir de esta ecuación diferencial parcial (The calculation of the volumetric expansion coefficient is done using this partial differential equation):

$\alpha = \frac{1}{V} \cdot \left(\frac{\partial V}{\partial T} \right)$

La siguiente fórmula se integra (The subsequent formula is integrated):

$\alpha\, dT = \frac{dV}{V}$

Se asume que el coeficiente permanece constante (Assuming the coefficient remains constant):

$\alpha \int\limits^{T_{f}}_{T_{o}}\,dT = \int\limits^{V_{f}}_{V_{o}}\, \frac{dV}{V}$

$\alpha \cdot (T_{f}-T_{o}) = \ln \frac{V_{f}}{V_{o}}$

El volumen al final es (The final volume will be):

$V_{f} = V_{o}\cdot e^{\alpha \cdot (T_{f}-T_{o})}$

El coeficiente de expansión volumétrica para acero es $12\times 10^{-6}\,^{\circ}C^{-1}$ (The volumetric expansion coefficient for steel is $12\times 10^{-6}\,^{\circ}C^{-1}$ ):

$V_{f} = (0.004\,m^{3})\cdot e^{(12\times 10^{-6}\,^{\circ}C^{-1})\cdot (50^{\circ}C-20^{\circ}C)}$

$V_{f} \approx 4.001\times 10^{-3}\,m^{3}$

Finalmente, la expansión que sufre el balín es (Finally, the expansion experienced by the pellet is):

$\Delta V = 4.001\times 10^{-3}\,m^{3} - 4.000\times 10^{-3}\,m^{3}$

$\Delta V = 1.440\times 10^{-6}\,m^{3}$

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Complete Question

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