Pure Substances Thermodynamics Professor Lee Carkner Lecture 5

PAL # 4 First Law  Pumping water uphill and then running it back to produce energy  Rate of power imparted to water =  W’ water = (1000)(2)(9.8)(40) =  But the pump and the turbine are only 75% efficient   pump = W’ water /W’ pump  W’ pump = 785/0.75 =  Cost per year = (1046)(10)(0.03)(365) = $   turbine = W’ turbine /W’ water  W’ turbine = (785)(0.75) =  Revenue per year = (785)(10)(0.08)(365) = $  Net Yearly Profit =

PAL # 4 First Law  Should you build it?  No    

Pure Substances  A pure substance consists of either a single type of atom or molecule or a homogeneous mixture   Can exist as a mixture of phases  Gas   Liquid   Solid  Strong intermolecular forces, high density, fixed molecular position

Types of Phases  Compressed liquid   Saturated liquid   Saturated Vapor   Saturated liquid and vapor can coexist together  Superheated vapor 

Saturation  A substance changes phase when it is at the saturation temperature for a given pressure   Can be compiled in tables for reference   T sat increases with P sat  Need more internal energy to become vapor at higher pressure

Change of T sat with P sat

Enthalpy   Defined as: h = u + Pv H = U +PV   Very useful for flow systems such as turbines

Specific Volume and Quality   Mass of saturated liquid = m f   Mass of saturated vapor = m g  Since both phases often co-exist we define the quality, x:  The quality is the relative fraction of the mixture in the vapor phase

Quality Relations  The total volume of a mixture is:  the volume occupied by each phase is:  We can use these relationships to write an expression for the combined specific volume of the mixture: v avg = v f +xv fg x = (v avg –v f )/v fg 

Property Diagrams  We will plot three key variables P, T, and v as:     Each region of the diagram represents a phase or mixture of phases

Pv Diagram

Pv Diagram Properties  Saturation curves define boundaries of liquid- vapor mixture region   Critical point is on the critical isotherm   Densities of both are the same  Above the critical point, no amount of pressure can condense the vapor to a liquid

Regions on a Pv Diagram

PT Diagram  Three curves can be drawn on the PT diagram  Fusion curve   Vaporization curve   Sublimation curve   The curves bound three distinct regions, one for each phase   Juncture of the three curves is the triple point where all three coexist

PT Diagram

Other PT Features  An isobar at standard atmospheric pressure intersects the normal boiling and melting points   The critical point is on the vaporization curve   Gas above critical T is called “gas”, below it is called “vapor” 

PvT Diagram for Water

PVT Diagram  P, V and T relations can be formed to create a three dimensional diagram   The PT and PV diagrams are formed by projection 

Next Time  Read:  Homework: Ch 3, P: 48, 54, 75, 86