Craig
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 Posted: Fri Aug 01, 2008 6:40 am Post subject: Re: Boltzmann>s constant is evil! |
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On Jul 31, 8:27 pm, Andrew Usher <k_over_hb...@yahoo.com> wrote:
[quote]On Jul 31, 7:55 pm, Craig <cager...@aol.com> wrote:
Suppose you add 200 J to 100 g of water. Suppose you have chosen a
scale such that this represents a change of "2 J" in water temperature
(since we have 100 g). Now, add 200 J to 100 g of iron (which has
approximately a tenth the heat capacity of water). This would raise
the temperature of the iron about 10 times as much. So, now the same
200 J causes a rise of "~20J" of iron temperature? The same amount of
energy gets converted into more "iron joules" than "water joules".
This clearly violates conservation of energy.
This is not how temperature works! You can>t divide Joules
by grams and get Joules!
[/quote]
This is exactly my point.
[quote]Actually, you>d need to divide the energy
by the heat capacity, then by the number of atoms or molecules
(more generally, formula units) to get the change in temperature.
[/quote]
As I understand your assertion, energy and temperature should both
have dimensions of energy.
So we>re all on the same page,
Heat = (Amount of stuff) * Heat capacity * DeltaTemperature
So, you want to work on an atomic/molecular scale, regardless of how
clumsy that may be on a macroscopic scale. Fine. Usually, I would
measure (Amount of stuff) in grams and use the specific heat
capacity. For you, we can measure (Amount of stuff) in molecules.
You stated elsewhere that heat capacity should be dimensionless. So
far, this is consistent: number of molecules * C * deltaT then works
out to have dimensions of T, which you assert should be energy.
Re-read what I wrote.
Divide the Heat (i.e. energy) by (Amount of stuff) * Heat capacity.
We all agree this should give a temperature. By your assertion,
(Amount of stuff) * Heat capacity ought to be dimensionless. This is
required to give temperature the same units as heat energy. However,
the point still stands that there is no consistent way to reconcile
the different changes in temperature of iron and water while claiming
that the Joules of Temperature are the *same* Joules that heat is
expressed in.
You might object that using molecular units means we should refer to
the molar heat capacity, rather than specific heat capacity. It is
interesting to note a certain regularity in the molar heat capacity of
solids (see: Law of Dulong and Petit). Despite this, many substances
(e.g. gases) do *not* obey this pattern. There is no "universal"
molar heat capacity. For example, the molar heat capacity of liquid
water is about three times larger than that for solid iron, both near
25 C. Suffice it to say, this potential red herring would not change
the essence of the argument. Temperature is *not* the same thing as
energy.
As a contrasting example, work and heat *are* the "same thing". I
could burn a fuel, release 100 J of heat, then use that heat to
generate, say, 20 J or work and 80 J of waste heat (or 10 J work + 90
J waste heat, etc. - always obeying a common sum). Or, I could exert
100 J of work against friction and deposit precisely 100 J of heat
into the sliding materials. In this case, Joules are Joules. They
indeed behave in a common way. Energy is conserved, one might say.
Temperature and energy do *not* behave like this. For example,
knowing that a material experienced a one degree rise in temperature
is *not* sufficient information to know how much energy was gained by
that unknown quantity of unnamed material.
- Craig |
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Matthew Johnson
Guest
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| Posted: Fri Aug 01, 2008 7:02 am Post subject: Re: Boltzmann>s constant is evil! |
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In article <9977d078-764d-4a8b-aeee-1f9b47f67ba7@p25g2000hsf.googlegroups.com>,
Andrew Usher says...
[snip]
[quote]They do, and what of it? This has nothing to do with the units
of heat capacity, which is dimensionless.
[/quote]
Dimensionless? How did you reach this conclusion? Specific heat capacity is
expressed in units of energy per degree of temperature per unit of mass.
In fact, energy and temperature can be expressed in units reciprocal to each
other, but this still does not make specific heat dimensionless. |
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Matthew Johnson
Guest
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| Posted: Fri Aug 01, 2008 7:02 am Post subject: Re: Boltzmann>s constant is evil! |
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In article <221a7beb-e33e-496d-96d4-d56f6e1f3632@59g2000hsb.googlegroups.com>,
Craig says...
[snip]
[quote]This becomes an untenable proposition. Temperature simply doesn>t
behave the same way energy does.
[/quote]
Not only that, but temperature>s units are reciprocal to those of energy. This
is clear from the modern, quantum mechanical definition as:
1/T = partial derivative of E w.r.t. Entropy.
Entropy, as the number of accessible quantum states, is dimensionless. |
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