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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.

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________ Gases

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  1. ________ 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

  2. ________ Factor also known as ________factor The curve for each gas becomes more ________as T  Modified by Jed Macosko

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. Partial Derivative Relations • Partial derivatives can be taken in __________. • Taking the inverse: • To find the __________partial derivative: • __________Rule: • and Modified by Jed Macosko

  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

  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

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