Energy Transfer in a Water and Aluminum Pan System

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The discussion revolves around calculating energy transfer in a system consisting of boiling water and an aluminum pan. For part A, the temperature of the water after mixing with the pan was determined, but there were challenges in part B regarding energy transfer from a stove. Participants suggested using the weighted average heat capacity and total mass of both the water and pan to find the correct energy transfer. Despite attempts to calculate the total energy using the formula deltaE = Q + W, the results were inconsistent, leading to confusion about the correct application of the equations. Clarification on the heat capacity values and mass calculations is needed for accurate results.
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Homework Statement



100 grams of boiling water (temperature 100° C, heat capacity 4.2 J/gram/K) are poured into an aluminum pan whose mass is 375 grams and initial temperature 24° C (the heat capacity of aluminum is 0.9 J/gram/K).
(a) After a short time, what is the temperature of the water?

(b) Next you place the pan on a hot electric stove. While the stove is heating the pan, you use a beater to stir the water, doing 1400 J of work, and the temperature of the water and pan increases to 74.6° C. How much energy transfer due to a temperature difference was there from the stove into the system consisting of the water plus the pan?


Homework Equations



deltaE=mC*deltaT
deltaE=Q+W

The Attempt at a Solution



Ok I got part A with no trouble but I'm struggling with part B. I tried using the mC*delta T equation for the water and the aluminum pan...adding those values and setting it equal to Q+W. I used 8.6 for delta T (74.6-66) since I got 66 degrees for my answer in part A. I then subtracted W to find Q in the second equation but it's not the correct answer. I think what might be throwing me is that the system consists of the water and pan. Any suggestions?
 
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You didn't say what value of C you used in the second calculation. But C' should be the weighted average of the mass of the water and the aluminium ( British spelling), and M' the sum of the masses.

C' = (C1*M1 + C2*M2)/(M1+M2)
M' = M1 + M2.

I think this will work, but I could be wrong.
 
Mentz114 said:
You didn't say what value of C you used in the second calculation. But C' should be the weighted average of the mass of the water and the aluminium ( British spelling), and M' the sum of the masses.

C' = (C1*M1 + C2*M2)/(M1+M2)
M' = M1 + M2.

I think this will work, but I could be wrong.

I calculated two values of mC*delta T, one for the water (100*4.2*8.6) and one for aluminum (375*0.9*8.6) and added those together and set that equal to Q+1400. I got Q=5115 (same answer as you) and it's incorrect.
 
how did u get a?
 

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