Mass of object during heat exchange

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Homework Statement



An aluminum container with a mass of 400 g contains 200 g of water at a temperature of 18°C. After a block of iron at a temperature of 90°C is placed in the water, the final temperature of the mixture changes to 28°C. Find the mass of the iron, assuming that there is no loss of heat to the surroundings.


Homework Equations



mass of aluminum = 0.40 g, heat capacity of aluminum = 910 J(kg.°C)
mass of water = 0.20 g, heat capacity of water = 4200 J
mass of iron = ? heat capacity of iron = 460 J

(delta)t = change in temperature

mAcA(delta)tA +mWcW(delta)tW + mIcI(delta)tI = 0



The Attempt at a Solution



This is the solution shown in the book:

(0.40 kg) x (910 J/(kg.°C)) x (28°C - 18°C) + (0.20 kg) x (4200 J/(kg.°C)) x (28°C - 18°C) + (mI) x (460 J/(kg.°C)) x (28°C - 90°C) = 0

3640 + 8400 - 28520 mI = 0
12040 = 28250 mI
mI = 0.422 kg


What I want to know is where they got 3640 and 8400 from, when 0.40 x 910 = 364 and 0.20 x 4200 = 840. Why did they add a zero? Is this an error in the book? I also do not know where 28 520 is from. What am I missing...
 

Answers and Replies

  • #2
rock.freak667
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(0.40 kg) x (910 J/(kg.°C)) x (28°C - 18°C) = 0.4 * 910*10 = 3640

You are forgetting to multiply by the change in temperature i.e. 10.
 
  • #3
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a block of aluminum 4 inch by 4 inch have and chamber of 1inch x 1 inch witch is heat faster the chamber or the whole block?
 
  • #4
rock.freak667
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You should start a new thread with your question with all the relevant equations and terms in it. Otherwise, you are hijacking another person's thread which I think your question is not related to the OP's question.
 
  • #5
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Hi Rock.freak667 what you mean I am hijacking onother person's thead,
I just like to find out if a 1inch diameter long 4 inch heat faster then all aluminum block
the block as reach the temperature of 100F can you help me ?
 
  • #6
rock.freak667
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Hi Rock.freak667 what you mean I am hijacking onother person's thead,
It means that you are posting a question in another person's thread which has nothing to do with your question.

I advise you to start a new thread following the template so that you can input your question and what equations you think will be relevant.

I just like to find out if a 1inch diameter long 4 inch heat faster then all aluminum block
the block as reach the temperature of 100F can you help me ?
If you are at a loss with what equation would be relevant, look up heat transfer by conduction, as that is what you are essentially wanting to know.
 
  • #7
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Thanks lot but do you know the answer? can you send to me? thanks
 
  • #8
rock.freak667
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Thanks lot but do you know the answer? can you send to me? thanks
As per the forum rules, no on at PF can just give you the answer. You need to show some attempt at finding the answer. Once more, please start a new thread.
 

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