Thermodynamics and Statistical Mechanics First Law of Thermodynamics.

Thermodynamics and Statistical Mechanics

First Law of Thermodynamics

Thermo & Stat Mech - Spring 2006 Class 3

2

Review of van der Waals Critical Values

227

278

3

ba

P

Rba

T

bv

C

C

C


3

van der Waals Results

bRa

Tba

Pbv ccc 278

271

3 2

bRa

R

bba

RTvP

c

cc

278

3271

2 375.0

83


4

van der Waals Results

Substance Pcvc/RTc

He 0.327

H2 0.306

O2 0.292

CO2 0.277

H2O 0.233

Hg 0.909


5

Configuration Work

đW = PdV

Gas, Liquid, Solid:


6

Kinds of Processes

Often, something is held constant. Examples:

dV = 0 isochoric or isovolumic processdQ = 0 adiabatic processdP = 0 isobaric processdT = 0 isothermal process


7

Work done by a gas

f

i

V

VPdVW

For isochoric process dV = 0, so W = 0For isobaric process dP = 0, so W = PV

đW = PdV


8

Work done by a gas


9

Work done by an ideal gas

f

i

V

VPdVW

For isothermal process dT = 0, so T = constant.

VRT

P


10

Isothermal Process

i

f

VV

V

V

V

VRTW

VRTW

VdV

RTW

f

i

f

i

ln

ln


11

Heat Capacity

Heat capacity measures the amount of heat that must be added to a system to increase its temperature by a given amount. Its definition:

where y is a property of the system that is kept constant as heat is added.

yy dT

QdC


12

Heat Capacity

Properties that are usually kept constant for a hydrostatic system are volume or pressure. Then,

PP

VV dT

QdC

dTQd

C

or ,


13

Heat Capacity

Clearly, the heat capacity depends on the size of the system under consideration. To get rid of that effect, and have a heat capacity that depends only on the properties of the substance being studied, two other quantities are defined: specific heat capacity, and molar heat capacity.


14

Specific Heat Capacity

Specific heat capacity is the heat capacity per mass of the system. A lower case letter is used to represent the specific heat capacity. Then, if m is the mass of the system,

P

PP

V

VV dT

Qdmm

Cc

dTQd

mmC

c

1

or ,1


15

Molar Heat Capacity

Molar heat capacity is the heat capacity per mole of the system. A lower case letter is used to represent the molar heat capacity. Then, if there are n moles in the system,

P

PP

V

VV dT

Qdnn

Cc

dTQd

nnC

c

1

or ,1


16

Shorter Version

PP

VV dT

qdc

dTqd

c

or ,

Use heat per mass.


17

cP – cV

đq = du + Pdv where u(T,v)

dvPvu

dTTu

qd

dvvu

dTTu

du

Tv

Tv


18

Constant Volume

dTdu

Tu

dTqd

cvv

v often ,


19

Constant Pressure

vPvu

cc

vPvu

cc

dTdv

Pvu

Tu

dTqd

Tvp

Tvp

PTvp


20

Ideal Gas

u is not a function of v.

Rcc vP


21

Adiabatic Process

For an ideal gas, and most real gasses,đQ = dU + PdV đQ = CVdT + PdV,.

Then, when đQ = 0, VC

PdVdT


22

Adiabatic Process

nRVdPPdV

CPdV

nRVdPPdV

dTnRPV

T

V

Then,

and ,

For an ideal gas, PV=nRT, so


23

Adiabatic Process

nRVdP

nRCCnR

PdV

nRVdP

nRCPdV

nRVdPPdV

CPdV

nRVdPPdV

dTnRpV

T

V

V

VV

0

110

Then,

and ,


24

Adiabatic Process

V

p

V

P

PV

V

V

C

C

VdPPdVVdPCC

PdV

CCnR

VdPC

CnRPdV

where,

0

0


25

Adiabatic Process

constant

constantlnlnln

constantlnln

,integrated becan which ,0

0

PV

PVPV

PVP

dPVdV

VdPPdV


26

Adiabatic Process

constant

constant

as, expressed be alsocan this

of help With the

constant

1

1

PT

TV

nRTPV

PV


27

for “Ideal Gasses”

33.162

1 :polyatomic

40.152

1 :diatomic

67.132

1 :monatomic

21

Thermodynamics and Statistical Mechanics First Law of Thermodynamics.

Documents

thermo stat mech spring

heat capacity heat capacity

gas slide

adiabatic process slide

pdv slide

isothermal process slide

heat capacity properties

constant volume slide