Heat and Conservation of Energy

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Homework Help Overview

The problem involves a heat transfer scenario where a punch bowl containing lemonade at 1.00 degree Celsius interacts with an ice cube at 0 degrees Celsius. The goal is to determine the final temperature of the system after the ice is added.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the heat lost by the lemonade and the heat gained by the ice, questioning the adequacy of the ice to cool the lemonade to zero degrees. There are inquiries about the calculations needed to determine the heat required to melt the ice and the heat released by the lemonade as it cools.

Discussion Status

Some participants have provided guidance on the calculations necessary for the problem, emphasizing the need to consider both the latent heat of fusion for the ice and the heat transfer for the lemonade. There is an ongoing exploration of the relationship between the heat gained and lost in the system.

Contextual Notes

Participants express uncertainty about when to apply the latent heat equation versus the heat transfer equation, indicating a need for clarification on these concepts. There is no explicit consensus on the approach to take, and multiple interpretations are being explored.

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Homework Statement



A large punch bowl holds 3.00 kg of lemonade (which is essentially just water) at 1.00 degree celsius. A 0.055 kg ice cube at 0 degrees is placed in the lemonade. What is the final temperature of the system?

Homework Equations


Q=mcΔT
Q=mL


The Attempt at a Solution


Having a hard time understanding the concept of heat lost and gained and when to use the latent heat equation in problems.
All I really know of how to start this out is Q(water) + Q(ice)=0
 
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Lemonade cools down, ice melts. Question is, is there enough ice to cool the lemonade to zero?
 
i have no clue tbh
 
I was trying to point you in the right direction, you took my comment too literally. Whether there is enough ice is a thing that has to be calculated.

How much heat is needed to melt the ice?

How much heat would you get from the water cooling it down to 0°C?
 
Borek said:
I was trying to point you in the right direction, you took my comment too literally. Whether there is enough ice is a thing that has to be calculated.

How much heat is needed to melt the ice?

How much heat would you get from the water cooling it down to 0°C?

ok so for this i need to use (mass of ice)(latent heat of fusion)and (mass of water)(latent heat of fusion) ?

i think this is somewhat on the right track. thank you sir for helping
 
Melting the ice is a process described by the latent heat equation.

Cooling down the water is a process described by the other equation, the one with ΔT.
 
ah right thanks. don't know why i thought of using the latent heat equation for the water. it's just cooling down, not changing phase
 

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