Equilibrium temperature of a mixture

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Homework Help Overview

The discussion revolves around determining the equilibrium temperature of a mixture involving steam and milk, with a focus on the heat transfer principles involved in the process. The original poster presents equations related to heat transfer but expresses uncertainty about their correctness and the resulting temperature calculation.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply heat transfer equations but questions the validity of their setup and logic, particularly regarding the temperature assumptions. Participants raise questions about the structure of the equations and the meanings of the terms involved, suggesting a need for clearer definitions and understanding of the heat transfer process.

Discussion Status

The discussion is active, with participants providing feedback on the original poster's equations and suggesting alternative approaches to framing the problem. There is a focus on clarifying the assumptions made in the equations and exploring the implications of those assumptions on the overall analysis.

Contextual Notes

Participants note that the original poster's calculations yield a temperature that does not match the expected answer, indicating potential misunderstandings in the setup of the problem. The discussion highlights the importance of accurately defining the heat transfer terms and their relationships in the context of the mixture.

frazdaz
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Homework Statement


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Homework Equations


[tex]Q = m c \Delta T \\<br /> Q = m L_v \\<br /> Q_{in} = Q_{out}[/tex]

The Attempt at a Solution


[tex]m_s c_s (100 - 8) + m_s L_v = m_s c_s (100 - T) + m_m c_s (T) \\<br /> 5778.06 + 33900 = 5778.06 - 62.805 T + 418.7 T \\<br /> 33900 = 355.895 T \\<br /> ∴ T = 95.25°C[/tex]
Answer should be 90. This particular working is using 8°C as a base but I've with absolute temperatures and still got the same answer so I'm guessing my logic is flawed?
Thanks
 
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Your first equation doesn't appear to be set up correctly. The left side has two terms and the right side has two terms.

Can you describe in words the meaning of each of the four terms in the equation?
 
TSny said:
Your first equation doesn't appear to be set up correctly. The left side has two terms and the right side has two terms.

Can you describe in words the meaning of each of the four terms in the equation?
Qin = extra thermal energy the steam has over the milk + heat to be released when the steam condenses
Qout = heat lost from the steam + heat gained by milk
 
The term

m[itex]_{s}[/itex]c[itex]_{s}[/itex](100-8)

implies that the mass of steam cools from 100 C to the temperature of the milk at 8 C after the steam condenses. This is clearly not the case, as the mixture will assume some as yet unknown temperature, which is higher than 8 C once thermal equilibrium is reached.

Rather than use Q[itex]_{in}[/itex] = Q[itex]_{out}[/itex], which is somewhat vague for this type of problem, why not use instead Q[itex]_{lost-from-steam}[/itex] = Q[itex]_{gained-by-milk}[/itex]
 
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