Thermo & Stat Mech - Spring 2006 Class 4 1 Thermodynamics and Statistical Mechanics Does the Internal Energy of a Real Gas Depend Only on Temperature?

Thermo & Stat Mech - Spring 2006 Class 4

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Thermodynamics and Statistical Mechanics

Does the Internal Energy of a Real Gas Depend Only on Temperature?

Thermo & Stat Mech - Spring 2006 Class 4

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Change of Phase

First Law is: du = đq – Pdv

For a finite change at constant temperature

u = q – Pv

At transition, u2 – u1 = l12 – P(v2 – v1)

l12 = (u2 + Pv2) – (u1 + P v1)

l12 = h2 – h1

Thermo & Stat Mech - Spring 2006 Class 4

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Enthalpy and Latent Heat

on)(sublimati vapor tosolid

ion)(vaporizat vapor toliquid

(fusion) liquid tosolid

13

23

12

hh

hh

hh

Enthalpy is defined as: h = u + Pv

Thermo & Stat Mech - Spring 2006 Class 4

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Enthalpy is a State Function

Thermo & Stat Mech - Spring 2006 Class 4

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Does u depend on Volume?

If u = u(T, v), then,

dvvu

dTTu

duTv

Thermo & Stat Mech - Spring 2006 Class 4

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From Cyclical Relation

uv

T

v

T

v

T

u

vT

cvu

cvu

Tuvu

vT

Thermo & Stat Mech - Spring 2006 Class 4

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Gay-Lussac–Joule Experiment

Thermo & Stat Mech - Spring 2006 Class 4

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Gay-Lussac–Joule Results

3-m kilomoleK 001.0

0

u

u

vT

vT

Thermo & Stat Mech - Spring 2006 Class 4

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Joule-Thompson Throttling Process

A gas passes through a constriction from a region where it is at high pressure to a region where it is at lower pressure. The gas expands, and the temperature of the gas can be lowered. This is an important tool in low temperature physics.

Thermo & Stat Mech - Spring 2006 Class 4

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Joule-Thompson Throttling Process

Thermo & Stat Mech - Spring 2006 Class 4

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Joule-Thompson Throttling Process

On high pressure side: Wi = – PiVi

On low pressure side: Wf = + PfVf

Total work: W = PfVf – PiVi

Q = 0 = U + W0 = Uf – Ui + PfVf – PiVi

0 = (Uf + PfVf ) – (Ui + PiVi )

Thermo & Stat Mech - Spring 2006 Class 4

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Enthalpy

vdPdhqd

VdPQddH

QdPdVdU

PdVQddU

VdPPdVdUdH

PVUH

so

law)(First

Thermo & Stat Mech - Spring 2006 Class 4

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Enthalpy

PPP

cdTdh

dTqd

vdPdhqd

Thermo & Stat Mech - Spring 2006 Class 4

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Enthalpy

hP

TThP

TP

TP

dPdT

cPh

Ph

dPdT

c

dh

dPPh

dTcdPPh

dTTh

dh

PThh

or 0

,0For

),(For

Thermo & Stat Mech - Spring 2006 Class 4

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Enthalpy

)( 0, If

t coefficienThomson -Joule

Phh

cPh

dPdT

PT

h

True for ideal gas.

Thermo & Stat Mech - Spring 2006 Class 4

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Ideal Gas

dTdu

c

dTdh

dTdh

c

V

PP

Thermo & Stat Mech - Spring 2006 Class 4

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Joule-Thompson Throttling Process