Page 120 - Mechanical Engineers' Handbook (Volume 4)

6 Relations among Thermodynamic Properties 109

• Entropy change
S S 0
2 1
hence the name isoentropic or isentropic for this process
• Entropy generation
S S 2 Q
S 0 (reversible)
gen 1→2 2 1
1 T
A quasistatic isothermal process 1 → 2 executed by a closed ideal-gas system in commu-
nication with a single temperature reservoir T is characterized by
• Energy interactions
2 2 V
Q W mRT ln 2
1 1 V 1
• Path
T T T 2 (constant) or PV P V P V 2 (constant)
1
1
1
2
• Entropy change
V
S S mR ln 2
2
1
V 1
• Entropy generation
S S 2 Q
S 0 (reversible)
gen 1→2 2 1
1 T
Mixtures of ideal gases also behave as ideal gases in the high-temperature, low-pressure
limit. If a certain mixture of mass m contains ideal gases mixed in mass proportions m , and
i
if the ideal-gas constants of each component are (c , c , R ), then the equivalent ideal gas
vi Pi i
constants of the mixture are
c mc
1
v
m i i v i
c
1
p
m i mc
i P i
R
1
ii
m i mR
where m m . i
i
One mole is the amount of substance of a system that contains as many elementary
entities (e.g., molecules) as there are in 12 g of carbon 12; the number of such entities is
23
Avogadro’s constant, N
6.022 10 . The mole is not a mass unit, because the mass of
0
1 mole is not the same for all substances. The molar mass M of a given molecular species
is the mass of 1 mole of that species, so that the total mass m is equal to M times the
number of moles n,
m nM
Thus, the ideal-gas equation of state can be written as