Finding the Final Temperature of Hot Coffee in a Cold Cup

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Homework Help Overview

The problem involves calculating the final temperature of hot coffee poured into a cold glass cup, focusing on the principles of thermal equilibrium and heat transfer. The context is within the subject area of thermodynamics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the heat lost by the coffee and the heat gained by the cup, questioning the underlying principles of heat transfer. Some express uncertainty about the appropriate equations to use, while others attempt to formulate a heat balance equation.

Discussion Status

Some participants have provided guidance on the concept of heat balance, and one individual has shared an equation they believe leads to the correct final temperature. However, there is no explicit consensus on the method or the final result, as others continue to explore different interpretations and approaches.

Contextual Notes

Participants note the assumption that no heat is lost to the surroundings, which is a critical aspect of the problem setup. There is also mention of confusion regarding the appropriate equations to apply, indicating a potential gap in understanding the relevant concepts.

rlc
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Homework Statement


(c11p34) You pour 160.0 g of hot coffee at 75.0 oC into a 230.0- g glass cup at 24.0 oC. If they come to thermal equilibrium quickly, what is the final temperature (in oC, enter deg in asnwer box)? Assume no heat is lost to the surroundings.

Homework Equations


(I don't even know, I've seen so many.)

The Attempt at a Solution


I've attempted this problem a couple times with different formulas, but none have worked.
Can someone just tell me what equation to use, please?
 
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Suppose the final temperature is Tf. Then the coffee has cooled off to that temperature and the cup has heated up. They tell you no heat is lost, so apparently it's to do with heat. Where did the heat from the coffee go and where did the heat for the cup come from ?
 
Thank you for replying! I actually tried another equation and found the correct answer:
(mass coffee)(Temp coffee-Tf)(4.18 J/gC)=(mass glass)(Tf-temp glass)(0.840 J/gC)
(160)(75-Tf)(4.18)=(230)(Tf-24)(0.840)
Tf=63.57 deg
 
It's what we call a heat balance. Heat given off = heat taken up. And you did well to include the cp.
 

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