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

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

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

________ of Gases P Real gases ________ … don’t they? P1 Pc P2 Vc Tc 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

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 3 solutions There is a point of ________ at the critical point, so… slope: curvature:  Modified by Jed Macosko 11/20/2018

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

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

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

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

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