## another temp prob

heres another one that my books getting me stumped on:
A 34.4 g of water at 65 ?C is mixed with 64.3 g of water at 25 ?C. Calculate the final temperature of the mixture.
it looks so easy but i can't seem to figure it out. do you just subtract the 65 from the 25 to get the temp change? if so then what about the g of water?
please help with this one and the one i sent before soon :? i need to understand these concepts fast.

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Well, if you think about it a bit more, subtracting the two temperatures makes no sense. Actually, what [i]really[/i] happens is an average. When you mix two materials at different temperatures, the resulting temperature is a [i]weighted[/i] average. So,

[(34.4 g)(65 ?C) + (64.3 g)(25 ?C)]/(34.4g + 64.3g) = 38.9 ?C

The expanation I provided was just an intitive reason for why the calculation is correct. A more formal reason involves the law of conservation of energy, which I can post you are interested in seeing it.

YES please post the law and an explanation of it i really need to understand this stuff by wendesday (finals) thank you soooo much for what you've done already it is much apreciated * sorry bout the spelling* :D

OK, it may be helpful to have an understand of what "temperature" is.

Humans have a sense of temperature - there are nerve endings in your skin which tell you if something is "hot" or "cold" when you touch it.
But this sense is rather subjective.
(eg, get three bowls of water - one hot, one cold, and one lukewarm.
Put your left hand in the hot water and your right hand in the cold water...hold them in there for a minute or two...
....then pull them out and stick them both in the lukewarm water -

your right hand will feel really warm, and your left hand will feel really cold - even though they're both now in the same temperature of lukewarm water! -) Basically your sense of temperature is a bit rubbish lol )

So, scientificially, we need to get a better definition of "temperature".
We say that "temperature" tells us whether energy can be transferred between two bodies as heat.

If two bodies are the same "temperature", then they are at "thermal equilibrium", and energy won't flow between them as heat.
If they are are different temperatures, energy will flow as heat from the hot one to the cold one.
(This is called the "Zeroth Law of Thermodynamics)

The "energy" we're talking about, which flows as what we call "heat", is, at a microscopic level, all the little molecules jumping and twisting and vibrating around.

However, different substances are made of differnent types of molecules,
and these different molecules have different abilities as to how much they can move around. (eg,some molecules are more tightly stuck together than others, some molecules are stiffer, others flex more, some like to rotate, others aren't so keen, etc etc)
The result of this is that different substances have what we call different "HEAT CAPACITIES".
The heat capacity is how much ENERGY the substance needs to change its TEMPERATURE by one degree.
(if a substance is made of molecules which don't like dancing, it will take a lot of heat energy to raise its temperature.... if the molecules are more perky and fly, just a few joules of heat energy will change their temperature more easily).

Heat Capacity is an inherent property of a substance.
So all water, whether a bucket or an ocean, has the same characteristic heat capacity (per kilogram of mass, or per moles of amount)

Something else, for example lead, turnips, or treacle, will have quite a different heat capacity.

Anyway, your questions seem to be mixing the SAME substance, so they have the same heat capacity.
So you only then have to consider how much there is (kg)

### cool

uuhh. ok. i get the heat thing its the diferent formulas for it that freak me out. :shock: but that did clear up some other questions i had concerning heat and what it was and does. THANK YOU!!! also what the heck is treacle???? :?

WebElements: the periodic table on the WWW [http://www.webelements.com/]