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

Specific Volume of Wet Mixture

More Properties of Wet Mixture

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

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:

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 273.17 & 0.6113 647.3 & 22.12 Mercury 234 & 5.0166 ~1546 Copper 1376 & 0.000079 8280 Silver 1234 & 0.01

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.

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

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.

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.

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.

Pressure Volume Diagram

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 = 0.5658 J-m3/mole2; b = 3.049x10-5 m3/mole,

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.

Van der Waals EOS a, b are the Van der Waals constants for the particular gas; for water: a = 0.5658 J-m3/mole2; b = 3.049x10-5 m3/mole,

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

Van der Waals Isotherms

Isotherms of Real Gases

Improved Cubic Equations of State

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

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.

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)

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

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):

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