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Re: [Phys-L] Temperature for the calorie?



On 01/27/2016 06:26 PM, Peter Schoch wrote:

Today I was asked about the calorie. Yes, we did the typical definition:
the amount of energy needed to raise 1 gram of water 1 degree Celsius.

A student, a Chemistry major, raised her hand and asked "At what
temperature?" She wanted to know was it at STP and then raised 1 degree,
or was it at 20 or 25 C...? It seemed a reasonable thing to ask,

Exceedingly reasonable, and indeed commendable. It's nice to see
some actual reasoning going on.

The relevant temperature is /approximately/ 15 or 20 °C, depending
on as-yet-unspecified details. You could work out a more precise
answer, but it would definitely not be worth the trouble, for the
following reasons:

0) The exciting thing about defining the calorie is that there
are so many definitions to choose from. It is *not* an SI unit.
It is not well standardized.

1) My main recommendation is to not bother with calories at all.
Stick to joules. Nobody in their right mind uses calories, so
it's not worth fussing over the exact definition.

Then you get to have a *separate* discussion about the heat
capacity of water. Water is *approximately* 4.2 joule per gram
and *approximately* 4.2 joule per cc over a wide range ... but
it's not constant.

Once you start asking about temperature, you also have to ask about
lots of other things. The heat capacity depends on pressure more
strongly than you might have guessed. Also it depends on what's
dissolved in the water. And of course physics deals with lots of
substances that have got nothing to do with water ... which is yet
another reason to not bother with calories.

If you want to calculate the heat capacity of water, I suggest
using the formula here:
http://webbook.nist.gov/cgi/cbook.cgi?ID=C7732185&Type=JANAFL&Plot=on#JANAFL

I've seen various web apps such as
http://www.peacesoftware.de/einigewerte/wasser_dampf_e.html
but I have *not* verified their accuracy.
I actually own a _Steam Tables_ book but it is not available at
the moment. Given a trustworthy table (or formula) you can find
various (T,P) combinations where the heat capacity takes on your
favorite value (calorie-related or otherwise).

2) If you insist on using calories for whatever reason, I
suggest using the "thermochemical calorie". It does not depend
on the properties of water at all; it is just 4.184 J period.

Finding a (T,P) combination where the heat capacity takes on this
value is a curiosity, not part of the definition.

I have no idea where the 4.184 J value comes from. There is
probably some interesting history, but I don't know it.

3) Meanwhile, if you choose the "15 degree" calorie instead of the
thermochemical calorie then the answer is obvious by definition:
it involves raising the water from 14.5 to 15.5 °C under standard
atmospheric pressure.

Again, nobody in their right mind uses calories anyway, so this
calorie is as good as any other.

4) Always remember that a "food calorie" is 1000 times larger
than a physics or chemistry calorie.