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Nonamiya [84]
2 years ago
7

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

?
Physics
1 answer:
Brrunno [24]2 years ago
0 0

Answer:

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

Explanation:

El coeficiente de expansión volumétrica se calcula a partir de la siguiente ecuación diferencial parcial (The volumetric expansion coefficient is computed by means of the following partial differential equation):

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

Se integra la fórmula a continuación (The formula is integrated herein):

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

Supóngase que el coeficiente es constante (Let suppose that coefficient is 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 final es (The final volume is):

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

El coeficiente de expansión volumétrica del acero es 12\times 10^{-6}\,^{\circ}C^{-1} (The volumetric expansion coefficient of 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 dilatación experimentada por el balín es (Lastly, the dillatation experimented 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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