thermodynamics and statistical mechanics review for quiz 1

Thermodynamics and Statistical Mechanics

Review for Quiz 1

Thermo & Stat Mech - Spring 2006 Class 11

2

Laws of Thermodynamics

First law: đQ – đW = dU

Energy is conserved


3


Second Law: The entropy of an isolated system increases in any irreversible process and is unaltered in any reversible process. This is the principle of increasing entropy.

S 0


4


Third Law: The entropy of a true equilibrium state of a system at a temperature of absolute zero is zero.

Equivalent to: It is impossible to reduce the temperature of a system to absolute zero using a finite number of processes.


5

Second Law Variations

No series of processes is possible whose sole result is the absorption of heat from a thermal reservoir and the complete conversion of this energy to work.

There are no perfect engines!


6

Second Law Variations

No series of processes is possible whose sole result is the transfer of heat from a reservoir at a given temperature to a reservoir at a higher temperature.

There are no perfect refrigerators!


7

Zeroth Law

If two systems are separately in thermal equilibrium with a third system, they are in thermal equilibrium with each other.


8

Work done by a gas

f

i

V

VPdVW

PdVdW

AdsAF

dW

FdsdW


9

Ideal gas law

Ideal gas law:PV = nRT

In terms of molar volume, v = V/n, this becomes:

Pv = RT, or P = RT/v


10

van der Waals equation of state

RTbvva

P

va

bvRT

P

2

2 or , Then,

This equation has a critical value of T which suggests a phase change. The next slide shows graphs for several values of T .


11

Thermal Expansion

Expansivity or Coefficient of Volume Expansion, .

TVTTV

V

PT

Tv

vTV

V

P

PP

),(

11


12

Compressibility

Volume also depends on pressure.

Isothermal Compressibility:

PVPPV

V

PTPV

V

T

T

),( 1


13

Cyclical Relation

1

0

PVT

VTP

VTP

VT

TP

PV

TP

PV

TV

TP

PV

TV


14

Carnot Cycle

A Carnot cycle is an idealized reversible cycle that operates between two heat reservoirs at temperatures T1 and T2, where T2 > T1. It can operate as a heat engine, or a refrigerator.


15

Thermal Efficiency ()

2

12

2

1

2

1

2

12

2

1

1

TTT

TT

Q

Q

Q

QQ

Q

W

If T1 = 0, = 1 (100%)


16

For a Carnot Engine

TQTT

Q

Q

1

2

1

2

1

2

1

2

TT

QQ or 0

2

2

1

1 TQ

TQ


17

Entropy

0 TQd

TQd

i i

i

dSTQd

For reversible processes.Entropy is a state variable.


18

First and Second Laws

First Law: dU = đQ – đW

First law, combined with the second law:

dU = TdS – PdV


19

Tds Equations

dPc

dvv

cdP

P

Tcdv

v

TcTds

dPTvdTcdPT

vTdTcTds

dvT

dTcdvT

PTdTcTds

vP

vv

PP

PP

P

vv

v


20

Ideal Gas

RccTPv

PT

Tvcc

Tvcc

vp

vp

vp

2

2

1


21

Properties

From first law: TdS = dU + PdV, or

Internal Energy dU = TdS – PdV U(S, V)

Enthalpy: H = U + PV

dH = TdS + VdP H(S, P)


22

New Potentials

Helmholtz Function:

F = U – TS

Gibbs Function:

G = U – TS + PV

G = H – TS

G = F + PV


23

All Four

dU = TdS – PdV U(S, V)

dH = TdS + VdP H(S, P)

dF = – PdV – SdT F(V, T)

dG = – SdT + VdP G(T, P)


24

Maxwell Relations

PTPS

VTVS

T

V

P

S

S

V

P

T

T

P

V

S

S

P

V

T


25

Clausius-Clapeyron Equation

liquid-Solid )(

vapor-Solid )(

vapor-Liquid )(

12

12

13

13

23

23

vvTdT

dP

vvTdT

dP

vvTdT

dP

thermodynamics and statistical mechanics review for quiz 1

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