The equation can be written as
lnK p T
ð Þ þ ln
p
p 0
À
P
m i
¼ ln
Y
i
x
m i
i
or
Y
i
x
m i
i ¼
p
p 0
À
P
m i
K p T
ð Þ
ð185Þ
This is known as the law of mass action.
Problem
9:1 Show that the internal energy of a material whose equation of state has the
form p = f(V)T is independent of the volume and the pressure. That is
@U
@V
T
¼ 0
@U
@p
T
¼ 0
9:2 Thermodynamicists sometimes refer to the “first TdS equation” and the
“second TdS equation”:
Tds ¼ Nc V dT þ Tb = j T
dV
Tds ¼ Nc p dT À TVbdp
Derive these equations.
9:3 Use the second TdS equation to show that
c p À c V ¼
Tvb
2
j T
9:4 Obtain the Helmholtz equation
@U
@V
À Á
T
¼ T
2 @
@T
p
T
À Á
V
from
@
@T
1
T
@U
@V
þ
p
T
!
&
'
V
¼
@U
@V
1
T
@U
@T
!
&
'
T
9:5 Consider a composite system made of two subsystems of two ideal gases
with the same mole number N
(1) = N
(1) = 3 kmol and with c v
(1) = (5/2)R and
c v
(2) = (3/2)R. The initial temperatures of the two subsystems are T i
(1) =
9.9 Chemical Equilibrium (Gaseous Reaction Product Composition)
271