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Heat exchange in a bath

  • Thread starter Karol
  • Start date
1,380
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1. Homework Statement
An aluminum vessel of 500 gr contains 117.5 gr water at 200C. a piece of iron of mass 200 gr and 750C is thrown inside. what's the final temperature and the water equivalent of the vessel.

2. Homework Equations
Specific heat of aluminum: 0.217
Specific heat of iron: 0.113

3. The Attempt at a Solution
##(500\cdot 0.217+117.5)(t-20)=200\cdot 0.113 (75-t)\rightarrow t=25^0##
The answer should be 230C.
The water equivalent:
##500\cdot 0.217=m=108.5 gr##
The answer should be 110 gr
 

NascentOxygen

Mentor
9,232
1,062
I make it 25°. The difference may be explained by use of S.H. values slightly different from those used by the textbook authors?
 

Simon Bridge

Science Advisor
Homework Helper
17,823
1,637
I'm seeing slightly different values for relative specific heats depending on where people round off or what standard they use or something or other.
I'm also thinking - check the book values from the chapter or any examples they give.
 

NTW

302
26
For the aluminum container..... 500 g * 0,217 * 293 K = 31791
For the water............................ 117,5 g * 1 * 293 K = 34428
For the iron............................... 200 g * 0,113 * 348 K = 7865

Total .................................................................... = 74084

Now, 74084 / ((500 *0,217)+(117*1)+(200*0,113)) = 298,6 K = 25,6 ºC
 
1,380
22
I don't know this equation: mass (x) specific heat (x) deg. kelvin, what are the units of the result? calories? or is it just a mathematical trick, some kind of a mean.
I only know: mass (x) specific heat (x) [itex]\Delta t[/itex]
 

NTW

302
26
I don't know this equation: mass (x) specific heat (x) deg. kelvin, what are the units of the result? calories? or is it just a mathematical trick, some kind of a mean.
I only know: mass (x) specific heat (x) [itex]\Delta t[/itex]
It's a 'weighted mean'. Useful for a lot of things. The units don't matter, but they are cal, since [grams * (cal/(grams * K)) *K] simplify to cal...
 
1,380
22
Thanks
 

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