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Find the equilibrium temperature in a mixture of 10 grams of water at 20 degrees and 50 grams of oil at 25 grams.

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Answer to a math question Find the equilibrium temperature in a mixture of 10 grams of water at 20 degrees and 50 grams of oil at 25 grams.

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Tiffany
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102 Answers
Para calcular la temperatura de equilibrio en una mezcla de dos sustancias, podemos utilizar la ley de conservación de la energía calorífica:

m_1c_1(T_f - T_1) = -m_2c_2(T_f - T_2)

Donde:
- m_1 y m_2 son las masas de las sustancias.
- c_1 y c_2 son los calores específicos de las sustancias.
- T_1 y T_2 son las temperaturas iniciales de las sustancias.
- T_f es la temperatura de equilibrio.

En este caso, tenemos:
- Agua: m_1 = 10 g, c_1 = 1 cal/g°C, T_1 = 20 °C.
- Aceite: m_2 = 50 g, c_2 = 0.5 cal/g°C, T_2 = 25 °C.

Sustituyendo en la ecuación de conservación de calor y despejando T_f:

10 \cdot 1 \cdot (T_f - 20) = -50 \cdot 0.5 \cdot (T_f - 25)

10(T_f - 20) = -25(T_f - 25)

10T_f - 200 = -25T_f + 625

35T_f = 825

T_f = \frac{825}{35} = 23.57

Entonces, la temperatura de equilibrio en la mezcla será de 23.57 °C.

\textbf{Respuesta:} La temperatura de equilibrio en la mezcla será de 23.57 °C.

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