REPLY Meaning of Stock/Level (SD6976)

[SDMAIL Jay Forrest]

Posted by  "Jay Forrest" <systems at jayforrest.com>

Hi Kim!

While I am not a physicist, I am a chemical engineer which requires a
significant level of thermodynamics so I feel at least partially qualified
to address your comments.

The concept of temperature relates to an intensive property that has subtle
nuances that lead it to be easily misconstrued. Intensive properties are
properties that describe the specific characteristics of a substance in a
given state and are independent of the amount of substance considered.
(Densiy is another intensive property that my be more easily comprehended).
In Thermodynamics by Lewis and Randall, temperature is "qualitatively
defined as follows: If there can be no thermal flow from one body to
another, the bodies are at the same temperature, but if one can lose
temperature to the other by thermal flow, the temperature of the former is
greater." The authors then go on to build a quantitative set of rules for
temperature that basically says the same thing as comprehensive rules
covering all cases. It is not about heat content per se but about conditions
that result in heat flow.

The most obvious failing of temperature as a stock lies in boiling water.
One places a pan of water over a flame. Being colder that the flame, the
water absorbs energy and warms - until it reaches the boiling point
(nominally 100 C at sea level). At that point the water continues to absorb
heat but does NOT increase in temperature and the temperature fo the steam
is still 100 C but has much greater heat content.

Temperature is an arbitrary measure related to the heat contained in a unit
of matter. It is important to not consider it an extensive property or
universal. Heat capacities (the amount of energy required to raise the
temperature of a substance by a fixed amount) are not consistent, either
across materials or even within a given material (i.e. the heat capacity
varies with temperature). 

As I alluded previously with a given substance and a narrow (fuzzy word)
range temperature can be somewhat "stocky". If we mix liquid water at one
temperature with liquid water at another the resulting temperature will be
pretty close to a weighted average of the component temperatures (1 cup of
water at 50 degrees added to 1 cup at 60 degrees will give 2 cups at
essentially 55 degrees. But Aluminum has a heat capacity about 1/4 that of
Iron such that if we have a pound of Aluminum at 600 degrees and a pound of
iron at 100 degrees and place them in contact and insulate them so they have
no external heat losses, you would end up with them both at 200 degrees.

A similar problem arises if we add a small amount of water at 40 degrees to
a block of ice at 0 C. The result will be at 0 C. The conservation principle
of stocks is defied. The reason is that temperature doesn't flow... Thermal
energy flows....

Hope this is helpful!
Jay Forrest
Posted by  "Jay Forrest" <systems at jayforrest.com>
posting date  Sun, 27 Apr 2008 08:48:34 -0500