1. Thermodynamics of Wet, Saturated & Superheated Vapor
P M V Subbarao
Professor
Mechanical Engineering Department
I I T Delhi
Insearch of Simple Pfaffian Substance …..

2. Specific Volume of Wet Mixture

3. More Properties of Wet Mixture

4. Let Y be any extensive property and let y be the corresponding intensive property, Y/m, then

5. Vapour Dome
Saturated Liquid Line and Saturated vapour line intersect at the critical point and form what is often called the “vapour dome.”
Water Critical Point:

6. Pressure – Temperature Diagram of a Pure Substance
Triple point
K & kPa
Critical Point
K & Mpa
Oxygen
54 & 0.15
154 & 5.04
Nitrogen
63 & 12.53
126.2& 3.39
Water
&
647.3 & 22.12
Mercury
234 &
~1546
Copper
1376 &
8280
Silver
1234 & 0.01

7. Vapour
Temperature of the substance is higher than the saturation temperature at a given pressure.
Pressure of the substance is lower than the saturation pressure at a given temperature.
Molecules of substance move in random paths.
Weak inter-molecular forces.
Occupy entire volume of the container : No free surface.
Very low density
Highly compressible.

8. p-v-T Relations for Vapour Phase
At high Temperature and low pressure pv is constant at a given temperature.
This nature is called Ideal gas behaviour of gases. T1 T2

10. Behaviour of Vapour  = interatomic potential, Joules.
r = separation of molecules, nm (mean Free path).
r = equivalent “hard sphere” radius of molecule (overlap of electron clouds).
At high T, high p, collisions in the repulsive part of – positive deviations from constancy.
At low T, moderate p, collisions in the attractive portion of  – negative deviations from constancy.

11. P – v- T Relation v = f (p,T) The specific volume of A vapour:
Greatest need for EoS of saturated and superheated steam.
R and a are constants.
The is called as Rankine’s Equation of state, 1849.

12. P – v- T Relation v = f (p,T) The specific volume of A vapour:
Callender’s Characteristic Equation for saturated and superheated vapours.
R and b are constants.
c is a function of temperature and it is called as co-aggregation volume.

13. Pressure Volume Diagram

14. Van der Waals EOS
One of the oldest but most extensively used of the EOS of non ideal gases
Any EOS model must reproduce graphs such as that of the previous
a, b are the Van der Waals constants for the particular gas;
for water: a = J-m3/mole2; b = 3.049x10-5 m3/mole,

15. JO H A N N E S D . V A N D E R W A A L S The equation of state for gases and liquids Nobel Lecture, December 12, 1910
I intend to discuss in sequence:
(1) the broad outlines of my equation of state and how I arrived at it;
(2) what my attitude was and still is to that equation;
(3) how in the last four years I have sought to account for the discrepancies which remained between the experimental results and this equation;
(4) how I have also sought to explain the behaviour of binary and ternary mixtures by means of the equation of state.

16. Van der Waals EOS
a, b are the Van der Waals constants for the particular gas;
for water: a = J-m3/mole2; b = 3.049x10-5 m3/mole,

17. Van der Waals Coefficients
Gas
a (Pa m3)
B (m3/mol)
Helium
3.46 x 10-3
23.71 x 10-6
Neon
2.12 x 10-2
17.10 x 10-6
Hydrogen
2.45 x 10-2
26.61 x 10-6
Carbon dioxide
3.96 x 10-1
42.69 x 10-6
Water vapor
5.47 x 10-1
30.52 x 10-6

18. Van der Waals Isotherms

19. Isotherms of Real Gases

20. Improved Cubic Equations of State

21. The constants a, b, c, Ao, Bo varies with substance

23. Compressibility Factor
The deviation from ideal gas behaviour can also be expressed by compressibility factor, Z.
The ratio of volume of real gas, Vreal to the ideal volume of that gas, Vperfect calculated by ideal gas equation is known as compressibility factor.

24. Compact description of non-ideality: the compressibility factor,
Z  1 as p  0 (ideality)
Z < 1 at low T, moderate p (point A)
Z > 1 at high p, high T (point B)

25. Generalized Compressibility Chart
Reduced Temperature TR = T/Tc
Reduced Pressure pR = p/pc

26. VdW EOS & Compressibility
a represents the attractive part of the potential; with b = 0, the VdW EOS gives a smaller v for the same T than the ideal gas
b represents the repulsive portion of the potential; with a = 0, the VdW EOS gives a larger v for the same T than the ideal gas
The VdW EOS is easily expressed in the forms p(T,v) or T(p,v).
For the v(T,p) form, or, equivalently, Z(p,T):

27. The ideal gas equation of state may be written several ways.