Real GasesReal Gases

CO22

C – first liquid condensing

D – liquid- vapor mixture atPvap(20 C)

E – last vapor condenses

F – liquid/solid is much lesscompressible than a gas

van der Waals equation of statevan der Waals equation of statePhysically-motivated corrections to Ideal Gas EoS.y yFor a real gas, both attractive and repulsive intermolecularforces are present. Empirical terms were developed to help accountfor both.

Excluded volumenRTP

V b

1. Repulsive forces: make pressure higher than ideal gas

Excluded volume V nb

Volume of one molecule of radius r is Vm = 4/3 r3

Closest approach of two molecules with radius r is 2rClosest approach of two molecules with radius r is 2r.Excluded volume Vexc is 23 Vm = 8Vm for two molecules.

So we estimate that 4 moleculeb V L

van der Waals equation of statevan der Waals equation of statePhysically-motivated corrections to Ideal Gas EoS.y yFor a real gas, both attractive and repulsive intermolecularforces are present. Empirical terms were developed to help accountfor both.

Pressure depends wall collisions, both on frequencyd h i f

2. Attractive forces: make pressure lower than ideal gas

and their force.

Both scale as n/V, so we expect a pressure correction of theform a(n/V)2 giving the van der Waals Equation of State

nRT aP

form –a(n/V)2, giving the van der Waals Equation of State

2PV nb V

3D van der Waals eqn of state3D van der Waals eqn of state

T= T/Tc

van der Waals Isotherms near Tcvan der Waals Isotherms near Tc

v d W “loops” arev d W loops arenot physical. Why?

Patch up with Maxwellconstruction

van der Waals Isotherms, T/Tc

Real GasesReal Gasesvan der Waals EoS

SCFPan2

V2

V nb nRT

van der Waals EoS

Condensation Solid Liquid

Critical point

V2

Pc

Supercritical Fluid

Solid Liquid

PGas

PTriple point

T Tc

Critical Constants of Real Gases

ThermodynamicsThermodynamics

The study of energy and its transformations

Chapter 2Th Fi t L f Th d iThe First Law of Thermodynamics

Conservation of Energy

The total energy of the universe( i l t d t )(or an isolated system)

is constant

Basic Definitions• System - volume of interest

( i l b surroundingst

Basic Definitions

(reaction vessel, test tube, biological cell, atmosphere, etc.)– Surroundings- volume

id

surroundingssystem

Open System

EnergyMatter

outside systemp y

surroundingssystemEnergy

Open system - matter can pass between system & surroundings

Closed SystemClosed system - matter cannot pass between system & surroundings

surroundingssystemIsolated system - Neither matter nor energy can pass between system & surroundings Isolated Systemsurroundings

Energy, Work and HeatEnergy is the capacity to do work

E gy, W H

W k n li d f n li d

For an isolated system doing work reduces its energy, having work done on it increases its energy

Work - generalized force over a generalized displacement Mechanical work = force x distance; -fdx Mechanical work force x distance; fdx Expansion work = pressure x volume; -pdV Electrical work = emf x charge displacement; EdQ

Sign convention Sign conventionWork done by a system is negativeWork done on a system is positive

Work is the result of organized motion of molecules

Energy, Work and Heat (2)E gy, W H ( )

H i h h i i Heat is the change in energy in a system that is produced by a change in its temperaturein its temperature

Heat is the result of disorderedHeat is the result of disordered(thermal) motion of molecules

First Law of Thermodynamics U (internal energy) is the total energy of a

F L w f m y m

system (kinetic + potential) Change in energy from initial state, i, to final state, f, U,

isisU = Uf - Ui

Internal energy is a state functionV l f t t f ti d d l t t t Value of a state function depends only on current state of the system, not how you get there - path independentA ill b th th h t t f d k d As we will see, both the heat transfer and work done on a system definitely depend on the path followed

First Law of ThermodynamicsF L w f m y m

• U changes only by doing work or transferring heat to/from systemy– If work is done on the system (heat in), DU > 0– If system does work (heat out), DU < 0

Thi i li th t f i l t d t (th – This implies that for an isolated system (the universe), U is constant.

First Law of ThermodynamicsF L w f m y m

Mathematical statement of first law: Mathematical statement of first law

U = q + w» Where q = heat transferred to system» and w = work done on systemy

The first law is simply a statement of The first law is simply a statement of the conservation of total energy for a system

with defined energy inputs and outputs

Distinguish betweenDistinguish betweenSystem & Surroundings

Internal EnergyInternal Energy

Internal Energy (U) is the sum of all potential and kinetic energy for all

U is a state function

potential and kinetic energy for all particles in a system

U is a state functionDepends only on current state, not on path

U = Ufinal - Uinitial

ConcepTest #1ConcepTest #1

Which of the following is not a state function?

A Altitude A. Altitude B. Pressure C W kC. WorkD. Mass

ConcepTest #2ConcepTest #2

A system receives 575 J of heat from and delivers 325 J of work to its surroundings delivers 325 J of work to its surroundings. What is the change in internal energy of the system?y

A. +900 J B 250 J B. +250 J C. -250 JD. -900 J