AnswerMass of Aluminum: Calculating Heat Transfer to Reach Final Temp

[DrMcDreamy]

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

 

[tweety1234]

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

 

[DrMcDreamy]

Copper:
Q=mc$$\Delta$$T
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$$\Delta$$T
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?

 

[Borek]

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

Besides, watch your algebra:

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.

 

[DeeNos]

This question involves calculating heat transfer and final temperature using the specific heat capacities of aluminum and copper. The formula to use for this would be Q = mcΔT, where Q is the heat transferred, m is the mass of the object, c is the specific heat capacity, and ΔT is the change in temperature. To solve for the mass of the aluminum chunk, you can set up two equations using this formula for both the copper cube and the aluminum chunk, and then use the fact that the final temperature is the same for both objects. This will allow you to solve for the unknown mass of the aluminum chunk.