Solving for Ice: Coffee Cooling With Heat Exchange

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Homework Help Overview

The problem involves calculating the amount of ice needed to cool a given mass of coffee from 70.0°C to 60.0°C, using principles of heat exchange. The context is centered around thermodynamics, specifically the concepts of heat transfer and phase changes.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of heat transfer equations, questioning the relationship between the heat lost by the coffee and the heat gained by the ice. There is an exploration of the variables involved, particularly concerning the unknown mass of ice and the total heat exchange.

Discussion Status

The discussion is actively exploring the correct formulation of the heat transfer equations. Some participants have provided guidance on equating the heat lost by the coffee to the heat gained by the ice, while others are clarifying the need to account for the energy required to melt the ice and subsequently heat the resulting water.

Contextual Notes

Participants note the assumption of neglecting the heat content of the cup and the surroundings, which may influence the calculations. There is also recognition of the complexity introduced by having multiple variables in the equations.

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Homework Statement


You are given 2.5 102 g of coffee (same specific heat as water) at 70.0°C. In order to cool this to 60.0°C, how much ice (at 0.0°C) must be added? Neglect heat content of the cup and heat exchanges with the surroundings.


Homework Equations


Q=(m ice)(c ice)(delta T ice+ m ice)(Lf)
Q=(m coffee)(c coffee)(delta T coffee)


The Attempt at a Solution


If these are the right formulas I still have the problem that there are 2 variables, since I don't know Q or m ice.
 
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The Q's in both equations are the same, energy lost by coffee = energy gained by ice.
so you simply set the two equations equal to eahc other
 
do you mean (m ice)(c ice)(delta T ice+ m ice)(Lf)=(m coffee)(c coffee)(delta T coffee)?
 
Almost, remember ther is energy to melt the ice (which doesn't depend on temperature) and then the energy to heat the resulting water to the final temperature.
 

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