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Find the equilibrium temperature of a mixture of 10 grams of water and 50 grams of oil.

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Answer to a math question Find the equilibrium temperature of a mixture of 10 grams of water and 50 grams of oil.

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Sigrid
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Para encontrar la temperatura de equilibrio en una mezcla de dos sustancias, podemos utilizar la ecuación de equilibrio térmico:

m_1 \cdot c_1 \cdot \Delta T = -m_2 \cdot c_2 \cdot \Delta T

donde:
- m_1 y c_1 son la masa y el calor específico del agua,
- m_2 y c_2 son la masa y el calor específico del aceite,
- \Delta T es la diferencia de temperatura entre las dos sustancias.

Primero, calculamos las respectivas cantidades de calor específico de cada sustancia:
- Calor específico del agua: c_{\text{agua}} = 4.18 \, \text{J/g}^\circ \text{C}
- Calor específico del aceite: c_{\text{aceite}} = 2.0 \, \text{J/g}^\circ \text{C}

Sustituimos los valores en la ecuación de equilibrio térmico:

10g \cdot 4.18 \, \text{J/g}^\circ \text{C} \cdot \Delta T = -50g \cdot 2.0 \, \text{J/g}^\circ \text{C} \cdot \Delta T

Simplificamos la ecuación:

41.8 \, \Delta T = -100 \, \Delta T

Despejamos \Delta T :

141.8 \, \Delta T = 0
\Delta T = 0

Por lo tanto, la temperatura de equilibrio en la mezcla de 10 gramos de agua y 50 gramos de aceite es de \boxed{0^\circ \text{C}} .

\textbf{Respuesta:} \boxed{0^\circ \text{C}}

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