Equation of State

1. Equations of State
(EOS)
PRESENTED BY :
TANU SINGH SISODIA
M.PHIL(PHYSICS)

2. How are states represented?
 Mathematically
Relate state variables to describe
property of matter

3. Equations of state
 Mainly used to describe fluids
Liquids
Gases
 EOS can also describe solids

4. ABCs of gas equations
Avogadro’s Law
Boyle’s Law
Charles’ Law
 A
 B
 C

5. Avogadro’s Law
 At constant temperature and pressure
Volume of gas proportionate to amount of gas
V  n

6. Boyle’s Law
 At constant temperature and amounts
 Pressure inversely proportionate to Gas volume ,
P  1/V

7. Charles’ Law
 At constant pressure and amounts
Volume proportionate to temperature, i.e.
V  T
T is in Kelvins

8. Combining all 3 laws…
 V  (1/p)(T)(n)
 V  nT/p
 Rearranging, pV = (constant)nT
 Thus we get the ideal gas equation:
pV = nRT

9. Assumptions
Ideal gas particles occupy
negligible volume
Ideal gas particles have
negligible intermolecular
interactions

10. But sadly assumptions
fail…Nothing is ideal in this world…

11. Johannes Diderik van der Waals
 November 23, 1837
– March 8, 1923
 Dutch
 1910 Nobel Prize in
Physics

12. Van der Waals Equation
 In 1873 Modified from ideal gas equation
 Accounts for:
Non-zero volumes of gas particles
Attractive forces between gas particles
(attractive effect)

13. Van der Waals Equation
 Attractive effect
Pressure = Force per unit area of container
exerted by gas molecules
Dependent on:
 Frequency of collision
 Force of each collision
Both factors affected by attractive forces

14. Van der Waals Equation
Hence pressure changed proportional to
(n/V)2
Letting a be the constant relating p and
(n/V)2…
Pressure term, p, in ideal gas equation
becomes [p+a(n/V)2]

15. Van der Waals Equation
 Repulsive effect
Gas molecules behave like small,
impenetrable spheres
Actual volume available for gas smaller than
volume of container, V
Reduction in volume proportional to amount of
gas, n

16. Van der Waals Equation
Let another constant, b, relate amount of gas,
n, to reduction in volume
Volume term in ideal gas equation, V,
becomes (V-nb)

17. Van der Waals Equation
 Combining both derivations…
 We get the Van der Waals Equation

18. Virial Equations

19. Virial Equations
•B(T), is a function of temperature and is
called the "second virial coefficient.
•C(T) is called the third virial coefficient,
and so on

20. Virial Equations
 Most flexible form of state equation
Terms can be added when necessary
Accuracy can be increase by adding infinite
terms

21. Isothermal Equation of State
 The simplest isothermal EOS for a solid is
the bulk modulus or incompressibility, K
K = -V (∂P/∂V)
 This equation is only valid for P < K
 for a linearly increasing K
K = K0 + K0' P

22. Murnaghan - 1937
 The Murnaghan assumed that the bulk
modulus varies linearly with pressure
V = V0 (1+K'P/ K0)
Vinet EoS / 'Universal EoS' – 1986

23. Thermal Equation of State
 High-temperature Birch-Murnaghan EoS

24. THANK YOU