Statistical Thermodynamics Chapter 16

Ideal Gases

1L =1 dm3= 0.001 m3

1L=1000 cm3, cc, mL 1m3 =1000 dm3 =106 cm3

RTVPnRTPV

1

Chapter 16: The Properties of Gases

Gas Constant

2

Real Gases versus Ideal Gases

3

300 K

CH4

Van der Waals, Redlich-Kwong, Peng-Robinson

4

5

6

Van der Waals, Redlich-Kwong, Peng-Robinson

vdw ??

ethane at 400 K

ethane at 305.33 K

7

Experimental P-V isotherms of CO2

8

Cubic Equations of State describe both liquid and gaseous region

9

Critical values of Pc , Vc , and Tc for vwd EOS

Critical values of Pc , Vc , and Tc for R-K EOS

10

27

8 27

3 2 bRaT

baPbV ccc

The value of is constant !!

11

The constant values of EOS can be obtained from Pc and Tc

12

Law of Corresponding States (LOCS)

13

Based on LOCS, all gases have the same functional

14

Virial Equation of State

15

Experimental Determination of B2V

B2V and Temperature

16

Relationships between virial coefficients and intermolecular interactions

r

Lennard-Jones Potential

17

18

Divide both sides by

B2V and LOCS

19

xr/TkT B VH /*

@ T* | 3.2 , B2v (T*) =0

B*2V vs T* and Boyle Temperature

20

The second virial coefficient indicates the first deviation from ideal gas

21

Three contributions to attractive force

22

Hard-Sphere Potential

23

Square-Well Potential

24

Relationship between B2V and a, b coefficients in vdw EOS

25

Relationship between B2V and a, b coefficients in vdw EOS

drreNdrrNTB 2rTkc

A2

A6

B ]1[2 )1(2- )(

0v2

6

³³f

��� V

V

SS 1 / 66 ¢¢rTkc B

36

2

3 2

VS cNa A

32 3

ANb SV

26

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x 1