# Heat exchange in a bath

#### Karol

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 water equivalent:
$500\cdot 0.217=m=108.5 gr$
The answer should be 110 gr

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#### NascentOxygen

Mentor
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

Homework Helper
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

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

#### Karol

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) $\Delta t$

#### NTW

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) $\Delta t$
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...

Thanks