Thermodynamics and Statistical Mechanics

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

baP

RbaT

bv

C

C

C


3

van der Waals Results

bRaT

baPbv ccc 27

8 271 3 2

bRaR

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 = PdVGas, 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.

VRTP


10

Isothermal Process

i

f

VV

V

V

VV

RTW

VRTWVdVRTW

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

QdCdTQdC

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

CcdTQd

mmCc

1or ,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

CcdTQd

nnCc

1or ,1


16

Shorter Version

PP

VV dT

qdcdT

qdc

or ,

Use heat per mass.


17

cP – cV

đq = du + Pdv where u(T,v)

dvPvudT

Tuqd

dvvudT

Tudu

Tv

Tv


18

Constant Volume

dTdu

Tu

dTqdc

vvv often ,


19

Constant Pressure

vPvucc

vPvucc

dTdvP

vu

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

nRVdPPdVdT

nRPVT

V

Then,

and ,

For an ideal gas, PV=nRT, so


23

Adiabatic Process

nRVdP

nRCCnRPdV

nRVdP

nRCPdV

nRVdPPdV

CPdV

nRVdPPdVdT

nRpVT

V

V

VV

0

110

Then,

and ,


24

Adiabatic Process

V

p

V

P

PV

V

V

CC

VdPPdVVdPCCPdV

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

nRTPVPV


27

for “Ideal Gasses”

33.1621 :polyatomic

40.1521 :diatomic

67.1321 :monatomic

21

Thermodynamics and Statistical Mechanics

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