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Unformatted text preview: 93 3.3. IDEAL MIXTURES OF IDEAL GASES
k= cP
,
cv (3.236) N yi si = sM, s= (3.237) i=1 ρi
,
Mi
v
1
V
=
=
= vi Mi ,
=
ni
yi
ρi
V
∂V
=
= v = vM ,
=
∂ni P,T,nj
n ρ i = yi ρ = (3.238) vi (3.239) vi (3.240) if ideal gas Pi = yi P, (3.241) P = ρRT = RT
,
v (3.242) if ideal gas Pi = ρi RT = RT
,
vi (3.243) if ideal gas P
= u + P v = u + RT = hM,
ρ h = u+ (3.244) if ideal gas hi = o
hi , if ideal gas, hi = ui + (3.245) Pi
= ui + Pi v i = ui + P vi = ui + RT = hi Mi ,
ρi (3.246) if ideal gas T o hi = h298,i + ˆˆ
cP i(T ) dT = hi Mi , (3.247) 298 if ideal gas
T si = so ,i
298 +
298 ˆ
cP i (T ) ˆ
dT −R ln
ˆ
T yi P
,
Po (3.248) =s o
T,i
if ideal gas yi P
Po si = so − R ln
T,i = si Mi , (3.249) if ideal gas
N T yi so ,i
298 s=
i=1 +
298 ˆ
c P (T ) ˆ
dT − R ln
ˆ
T P
Po N − R ln y
yi i = sM. i=1 if ideal gas (3.250)
CC BYNCND. 18 November 2011, J. M. Powers. 94 CHAPTER 3. GAS MIXTURES 3.3.3 Amagat model The Amagat model is an entirely diﬀerent paradigm than the Dalton model. It is not used
as often. In the Amagat model,
• all components share a common temperature T ,
• all components share a common pressure P , and
• each component has a diﬀerent volume.
Consider, for example, a binary mixture of calorically perfect ideal gases, A and B . For
the mixture, one has
P V = nRT,
(3.251)
with
n = nA + nB . (3.252) P VA = nA RT,
P VB = nB RT. (3.253)
(3.254) PV
P VA P VB
=
+
.
RT
RT
RT (3.255) For the components one has Then n = nA + nB reduces to Thus
V = VA + VB ,
VA VB
+
.
1=
V
V 3.4 (3.256)
(3.257) Gasvapor mixtures Next consider a mixture of ideal gases in which one of the components may undergo a phase
transition to its liquid state. The most important practical example is an airwater mixture.
Assume the following:
• The solid or liquid contains no dissolved gases.
• The gaseous phases are all well modeled as ideal gases.
• When the gas mixture and the condensed phase are at a given total pressure and temperature, the equilibrium between the condensed phase and its vapor is not inﬂuenced
by the other component. So for a binary mixture of A and B where A could have both
gas and liquid components PA = Psat . That is the partial pressure of A is equal to its
saturation pressure at the appropriate temperature.
CC BYNCND. 18 November 2011, J. M. Powers. ...
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This note was uploaded on 11/26/2011 for the course EGN 3381 taught by Professor Parksou during the Fall '11 term at FSU.
 Fall '11
 ParkSou
 Dynamics

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