Direct Energy, 2018a

12 RELATING ENERGY CONVERSION PROCESSES 285
would take energy to restore the system to the ordered state. Both of these
systems can be described by the language of calculus of variations. As detailed
in the fourth column, temperature can be chosen as the generalized
path and entropy can be chosen as the generalized potential. Alternatively
asdetailed in the fth column, entropy can be chosen asthe generalized
path and temperature can be chosen as the generalized potential. Both
of these columns assume that the pressure and volume remain constant.
The quantity C v , which shows up in these columns, is the specic heat at
constant volume in units
J
, and it wasintroduced in Sec. 8.3.
g·K
The equation of motion that results when temperature is chosen as the
path and entropy ischosen asthe generalized potential isa statement of
conservation of entropy, and each term of thisequation hasthe unitsof
entropy. Thisrelationship ismore commonly known asthe second law of
thermodynamics, and it shows up in the second to last row of Table 12.7.
More commonly, the law is written for a closed system as [109, p. 236],
ˆ δQ
ΔS =
T + S produced. (12.22)
In words, it says the change in entropy within a control mass is equal to
the sum of the entropy out of the control mass due to heat transfer plus
the entropy produced by the system.
(change in entropy) =(entropy out due to heat)+(entropy produced)
A system can become more organized or more disordered, so ΔS may
be positive or negative. If energy is supplied in ´ or out, entropy can be
δQ
transfered in or out of a system, so the quantity may be positive or
T
negative.
Energy is listed in the third to last row of Table 12.7 in two dierent
forms. The rst expression is an integral expression. For example, you
can integrate the volume with respect to pressure to nd the energy of a
system.
ˆ
E = VdP (12.23)
Alternatively, the second expression
ΔE = VΔP (12.24)
can be used to nd change in energy in the case when volume is not a
strong function of pressure over a small element.