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Re: Strange "Energy" Units



At 10:53 AM 1/19/01 -0500, Peter Schoch wrote:
In the text, and in the lectures, they refer to energy transfer
(heat, soloar radiation, ocean pump, etc.) in units of W/m^2.

It appears there are three ideas in play
-- Conceptually, what is the physical quantity of interest?
-- What is the English name for this quantity?
-- What is the appropriate unit of measurement?

1) I can easily imagine many situations (heat transfer, solar radiation, et
cetera) where the fundamental physics involves transferring a certain
amount of energy per unit time per unit area. This is appropriately
measured in Watts per meter squared. This is what we call an "intensive"
quantity.

2) OTOH calling this fundamental physical process "energy transfer" is
problematic. Calling it "energy flux" would be much better.

When I questioned the Professor teaching the class about the units
("Shouldn't energy units be in Joules?"), he was perplexed because he
had always referred to energy in these units of W/m^2.

3) The confusion level is increasing. Previously it was energy _transfer_
in W/m^2. Now it has become simply _energy_ in W/m^2. This is a step in
the wrong direction.

4) Of course energy should be measured in Joules. This is what we call an
"extensive" quantity. There are many questions, especially specific
practical questions, that call for an answer in the form of an extensive
quantity. (This is in contrast to questions about the fundamental physical
processes, which often call for answers in the form of intensive quantities.)

Energy transfer _rate_ would be measured in J/sec.

5) Don't be too harsh on the aforementioned Professor. The physics
industry has done a rather poor job in inventing names for important
quantities. We do rather well with electrical quantities, but there are
anomalies even here:
English word symbol SI units
electric charge (conserved quantity) q C
charge density (on a capacitor plate) sigma C/m^2
charge density (space charge) rho C/m^3
electric current I A == C/sec
current density j A/m^2
local conservation law (d/dt) rho = - del . j

Note the overloading of the English term "charge density".

The corresponding situation for energy is not too bad, but alas
corresponding concepts do not have corresponding names:
English word symbol SI units
energy (conserved quantity) E J
energy density U J/m^3
power P W == J/sec
energy flux F W/m^2
local conservation law (d/dt) U = - del . F

However
a) power is sometimes called "energy flow" (which is harmless).
b) power is sometimes miscalled "energy flux" (in conflict with F above).
c) power symbol P conflicts with pressure symbol P and momentum symbol P
d) to carry the analogy to electrical nomenclature to an extreme, one
could imagine calling the power "energy current"... but I've never
heard anyone do that.
e) similarly, in analogy to current density, one could call the energy
flux the "power density"... That is in standard use in some circles,
but alas the term is overloaded: sometimes it means W/m^2 and
sometimes W/m^3.
f) there are other well-estabished concepts that have the same
dimensions, W/m^2, such as _intensity_. In some applications
(e.g. solar heating) such terms are very appropriate, but in
others (e.g. heat conduction) they would be inappropriate.

At 11:24 AM 1/19/01 -0800, Leigh Palmer insisted the W/m^2 should be:
...energy flux density! When we become picky, we must become very picky.
-------

Leigh is not alone in this usage; this is related to item (b) in the list
above. But I don't see what the attraction is.