1. Modified by Jed Macosko
________ Gases
have non-zero volume at low T and high P
have repulsive and attractive forces between molecules
short range, important at ________ P
longer range, important at ________ P
At low pressure, molecular volume and intermolecular forces can often be neglected, i.e. properties  ideal.
________ Equations
B is the second ________ ________. C is the third ________ ________. They are temperature dependent.
_____ ___ ______ Equation
Modified by Jed Macosko
11/20/2018

2. ________ Factor also known as ________ factor
The curve for each gas becomes more ________ as T  
Modified by Jed Macosko
11/20/2018

3. The van der Waals Equation 1
Intermolecular attraction = “________ pressure”
“molecular volume”  ________ volume
(do the algebra)
The initial slope depends on a, b and T:
________ size dominant
________ dominant
________ Temperature
______ for
______ at
~ ideal behaviour over wide range of P
Modified by Jed Macosko
11/20/2018

4. ________ of Gases P Real gases ________ … don’t they? P1 Pc P2 VcTc T2
supercritical fluid
liquid
gas
Tc, Pc and Vc are the ________ constants of the gas.
Above the ________ temperature the gas and liquid phases are continuous, i.e. there is no interface.
Modified by Jed Macosko
11/20/2018

5. The van der Waals Equation 2
The van der Waals Equation is not exact, only a model. a and b are ________ constant. P b
The ________ form of the equation predicts solutions
There is a point of ________ at the critical point, so…
slope:
curvature: 
Modified by Jed Macosko
11/20/2018

6. The Principle of Corresponding States
__________ variables are dimensionless variables expressed as fractions of the critical constants:
Real gases in the same state of _______ volume and _________ temperature exert approximately the same _________ pressure.
They are in corresponding states.
If the van der Waals Equation is written in reduced variables,
Since this is __________ of a and b, all gases follow the same curve (approximately). Z Pr
1.0
Tr = 1.5
Tr = 1.2
Tr = 1.0
Modified by Jed Macosko
11/20/2018

7. Partial Differentiation
for functions of more than one variable: f=f(x, y, …)
Take _______as an example
For an increase
y constant
x constant
For a simultaneous increase
In the limits
total differential
__________ differential
for a real single-value function f of two independent variables,
Modified by Jed Macosko
11/20/2018

8. Partial Derivative Relations
Partial derivatives can be taken in __________ .
Taking the inverse:
To find the __________ partial derivative:
__________ Rule:
and
Modified by Jed Macosko
11/20/2018

9. Partial Derivatives in Thermodynamics
From the __________ equation of state for a __________ system,
__________ partial derivatives can be written:
but given the ______ inverses, e.g
and the __________ rule
there are only two __________ “basic properties of matter”. By convention these are chosen to be:
the coefficient of __________ expansion (isobaric), and
the coefficient of __________ __________ .
The third derivative is simply
Modified by Jed Macosko
11/20/2018

10. The __________ Relation
Suppose
Is z an exact differential, i.e. dz?
cross-differentiation
dz is exact provided
because then
The corollary also holds (if exact, the above relations hold).
__________ functions have exact differentials.
__________ functions do not.
New thermodynamic relations may be derived from the __________ relation.
e.g. given that
it follows that
Modified by Jed Macosko
11/20/2018