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________ 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.

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gases
________ 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

factor
________ Factor

also known as ________factor

The curve for each gas becomes more ________as T 

Modified by Jed Macosko

the van der waals equation 1

Intermolecular attraction= “________pressure”

“molecular volume” ________volume

  • ______for
  • ______for
  • ______at

________size dominant

________dominant

________Temperature

~ ideal behaviour over wide range of P

The van der Waals Equation 1

(do the algebra)

The initial slope depends on a, b and T:

Modified by Jed Macosko

of gases

P

Pc

P2

Tc

P1

T2

T1

Vc

________ of Gases

Real gases ________ … don’t they?

supercritical fluid

gas

liquid

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

the van der waals equation 2

P

The ________form of the equation predicts 3 solutions

0

b

The van der Waals Equation 2

The van der Waals Equation is not exact, only a model. a and b are ________constant.

There is a point of ________at the critical point, so…

slope:

curvature:

Modified by Jed Macosko

the principle of corresponding states

Tr = 1.5

1.0

Tr = 1.2

Z

Tr = 1.0

Pr

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).

Modified by Jed Macosko

partial differentiation

y constant

x constant

For an increase

For an increase

In the limits

Partial Differentiation

for functions of more than one variable: f=f(x, y, …)

Take _______as an example

For a simultaneous increase

total differential

__________ differential

for a real single-value function f of two independent variables,

Modified by Jed Macosko

partial derivative relations
Partial Derivative Relations
  • Partial derivatives can be taken in __________.
  • Taking the inverse:
  • To find the __________partial derivative:
  • __________Rule:
  • and

Modified by Jed Macosko

partial derivatives in thermodynamics
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

the relation
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