Page 156 - Essentials of physical chemistry

118 Essentials of Physical Chemistry

FIGURE 6.6 An iodine enhanced fingerprint. (Photo provided courtesy of Forensics Source 2010.) Thanks to
Eric Schellhorn, director of marketing, and Floyd Wilson who developed a print on an outside rough surface as
a severe demonstration as requested. Close examination reveals clear print lines suitable for computer analysis.
See Ref. [3] for additional examples.

Recall

qU qU 1 qU qU qU qV
dV :
qT V qV T dT P qT P qT V qV T qT P
dU ¼ dT þ ) ¼ þ
Then

qU qU qV qV qU qV qU
þ P þ P :
qT qV qT qT qT qT qV
(C P C V ) ¼ þ ¼
V T P P V P T

qU qV R
Recall that for the ideal gas ¼ 0 and ¼ , which lead to C P C V ¼ R.
qV qT P
T P n¼1
However, this time we use one of the HUGA equations:

qU qS
dU ¼ TdS PdV and ¼ T P:
qV qV
T

qV qS qV qS
T T :
qT qV qT qV
(C P C V ) ¼ P þ P ¼
P T P T
That was pretty easy, but now we need another equation from the HUGA set dA ¼ SdT PdV

qS qP qV qP
and ¼ ,so (C P C V ) ¼ T .
qV qT qT qT
T V P V
We recognize these quantities as things we can measure in a laboratory but not the most convenient
expression for routine use. Next, we need a general expression of the volume differential (and set it
to zero for a new relationship): dV ¼ 0

qV

qV qV qP qT P
dP ¼ 0, :
qT qP qT qV
dV ¼ dT þ ¼
P T V
qP T