AnswerMass of Aluminum: Calculating Heat Transfer to Reach Final Temp

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Discussion Overview

The discussion revolves around a physics problem involving heat transfer between metallic objects and water within a steel container. Participants explore the calculations needed to determine the mass of an aluminum chunk based on the final temperature of the system remaining unchanged at 24°C.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents the problem and seeks guidance on the appropriate formula to use for calculating heat transfer.
  • Another participant reiterates the problem and provides the heat transfer equation Q = mcΔT, indicating the need to calculate heat for both copper and aluminum.
  • A participant calculates the heat lost by the copper and finds it to be -3671.1 J, but expresses confusion about how to proceed with the aluminum's heat transfer calculation without knowing Q.
  • Another participant suggests that the temperature remaining constant implies a relationship between the heat gained by aluminum and the heat lost by copper, hinting at the need for careful algebra in the calculations.

Areas of Agreement / Disagreement

Participants do not reach a consensus on how to proceed with the calculations, and there is uncertainty regarding the interpretation of the heat transfer relationships in the problem.

Contextual Notes

There are unresolved aspects regarding the assumptions made in the calculations, particularly how the heat transfer equations relate to the unchanged final temperature of the water and the implications for the mass of aluminum.

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Homework Statement



I think this is more of a gen chem question, but this is for my physics lecture.

A student drops two metallic objects into a 240 g steel container holding 62 g of water at 24◦C. One object is a 186 g cube of copper that is initially at 75◦C, and the other is a chunk of aluminum that is initially at 4.6◦C. To the student’s surprise, the water reaches a final temperature of 24◦C, precisely where it started. What was the mass of the aluminum chunk? Assume the specific heat of aluminum and copper is 900 J/kg ·◦C and 387 J/kg ·◦C,respectively. Answer in units of kg

Homework Equations



What is the formula that I am supposed to use for this? TIA
 
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DrMcDreamy said:

Homework Statement



I think this is more of a gen chem question, but this is for my physics lecture.

A student drops two metallic objects into a 240 g steel container holding 62 g of water at 24◦C. One object is a 186 g cube of copper that is initially at 75◦C, and the other is a chunk of aluminum that is initially at 4.6◦C. To the student’s surprise, the water reaches a final temperature of 24◦C, precisely where it started. What was the mass of the aluminum chunk? Assume the specific heat of aluminum and copper is 900 J/kg ·◦C and 387 J/kg ·◦C,respectively. Answer in units of kg

Homework Equations



What is the formula that I am supposed to use for this? TIA

Q = mcT
 
Copper:
Q=mc\DeltaT
Q=(.186 kg)(387 J/kg C)(24 C -75 C)
Q=-3671.1 J

Aluminum:
But I am not given Q, so I have to solve for 2 things: Q and m
Q=mc\DeltaT
Q=m(900 J/kg C)(24 C -4.6 C)
Qm=(900 J/kg C)(19.4 C)
Qm=17,460 J/kg
Which doesn't make sense.

So what do I do?
 
You are given Q for Al, although not directly - think, what it means that the temperature has not changed?

Besides, watch your algebra:

DrMcDreamy said:
Q=m(900 J/kg C)(24 C -4.6 C)
Qm=(900 J/kg C)(19.4 C)

Second doesn't follow from the first.
 

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