Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

TdS is not dQ or d(anything)



On 05/10/2003 12:14 PM, Bob Sciamanda wrote:
... the term TdS represents the heat transfer dQrev.

I know practically every reference writes
TdS "=" dQ
but it makes my skin crawl every time I see it.

TdS is a one-form, but it is not an _exact_ one-form,
except under verrrry special conditions, in which
case it is obligatory to explain what the special
conditions are. Reversibility is nowhere near special
enough; a Carnot engine is reversible but does not
have TdS "=" dQ or dQrev or d(anything).

Trying to find a Q such that TdS "=" dQ is exactly
like trying to assign a height to the water in an
Escher waterfall. This is why I worked so hard to
create diagrams of non-exact one-forms as discussed
in
http://www.monmouth.com/~jsd/physics/non-conservative.htm

For the connection to thermo, see
http://www.monmouth.com/~jsd/physics/thermo-forms.htm
(which is alas still quite drafty).

Also note that it is completely unnecessary to
write "dQ". Nobody every uses "dQ". Just express
TdS as TdS. If you want to integrate TdS along
some path, say exactly what the path is.