Too many particles… can’t keep track! - PowerPoint Presentation

Slide1

Too many particles… can’t keep track!Use pressure (p) and volume (V) instead.Temperature (T) measures the tendency of an object to spontaneously give up/absorb energy to/from its surroundings. (p and T will turn out to be related to the too many particles mentioned above)p, V, and T are related by the equation of state: f(p,V,T) = 0 e.g. pV = NkBTHeat is energy in transit and it is somehow related to temperature

Thermal Physics

Slide2

A

C

B

C

Diathermal wall

Zeroth law of thermodynamics

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

C can be considered the thermometer. If C is at a certain temperature then A and B are also at the same temperature.

Slide3

Temperature is related to heat and somehow related to the motion of particles

Need an absolute definition of temperature based on fundamental physics

A purely thermal physics definition is based on the Carnot engine

Can also be defined by statistical arguments

Slide4

Slide5

Combinatorial problem

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Slide6

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Slide7

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Microstates and Macrostates

Slide8

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Microstates and Macrostates

Slide9

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Microstates and Macrostates

All these microstates belong to the macrostate of 1 head in 100 coins

Slide10

Macrostate

Number of Microstates (

)

Slide11

n = 170;

x = 0:1:n;

y = factorial(n)./(factorial(x).*factorial(n-x));

figure;

plot(x,y);

Slide12

Each microstate is equally likelyThe microstate of a system is continually changingGiven enough time, the system will explore all possible microstates and spend equal time in each of them (ergodic hypothesis).

How is all this @#$%^& related to thermal physics?

Slide13

 

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Slide16

Big question:

How do we relate the number of microstates for a particular macrostate to temperature?

Slide17

E

1

E

2

At thermal equilibrium the temperature (whatever it is) will be the same for both systems. Total energy E = E

1 + E2 is conserved.

T1 < T2

But no particular relation for E1 and E2

+ E

-

E

Slide18

Slide19

clear all;n1 = 4;n2 = 8;e = 6;i = 0;for x = 0:1:n1y1 =(factorial(n1)./(factorial(x).*factorial(n1-x)));y2 = (factorial(n2)./(factorial(e-x).*factorial(n2-(e-x))));i=i+1;y(i)=y1*y2x1(i)=x;endfigure;plot(x1,y);

Slide20

Each microstate is equally likely

The microstate of a system is continually changing

Given enough time, the system will explore all possible microstates and spend equal time in each of them (ergodic hypothesis).

Slide21

Most likely

macrostate

the system will find itself in is the one with the maximum number of microstates.

Slide22

A

C

B

C

Diathermal wall

Zeroth law of thermodynamics

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

C can be considered the thermometer. If C is at a certain temperature then A and B are also at the same temperature.

Slide23

Most likely macrostate the system will find itself in is the one with the maximum number of microstates.

E

1

1(E1)

E22(E2)

E

(E)

System A

System C

Slide24

Most likely macrostate the system will find itself in is the one with the maximum number of microstates.

E

1

1(E1)

E22(E2)

E

(E)

Slide25

Ensemble: All the parts of a thing taken together, so that each part is considered only in relation to the whole.

Slide26

E

(E)

Microcanonical ensemble

: An ensemble of snapshots of a system with the same N, V, and E

Slide27

Microcanonical ensemble: An ensemble of snapshots of a system with the same N, V, and ECanonical ensemble: An ensemble of snapshots of a system with the same N, V, and T

E

11(E1)

E

2



2

(E

2

)