Equation of state

1. • UMAIMA AHMED17CH20
• HAMZA BHUTTA17CH21
• FERHAN ALI JARWAR17CH23
• M WAJAHAT ALI17CH25
• AFFAQUE QURESHI17CH27
• MANSOOR M KAPRI17CH29
17CH19 • M SIDDIQUE
MEHRAN UNIVERSITY OF ENGINEERING AND TECHNOLOGYJAMSHORO
THERMODYNAMICSASSIGNMENT
ASSIGNED BY :
PROF: DR.ZULFIQAR ALI
BHATTI

2. EQUATION OF STATE
 An equation showing the relationship between the
values of the pressure, volume, and temperature of a
quantity of a particular substance.
 In physics and thermodynamics, an equation of
state is a thermodynamic equation relating state
variables which describe the state of matter under a
given set of physical conditions, such
as pressure, volume, temperature (PVT), or internal
energy. Equations of state are useful in describing the
properties of fluids, mixtures of fluids, solids, and the
interior of stars.

3. TYPES OF EQUATIONS OF STATE
1. Vander Waals equation of state
2. Bealltie-Bridgeman equation of state
3. Benedict-Webb-Rubbin equation of state
4. Virial equation of state

4. VAN DER WAALS EQUATION
 In 1873, J. D. vander Waals introduced the first equation of state derived by the
assumption of a finite volume occupied by the constituent molecules. His new
formula revolutionized the study of equations of state, and was most famously
continued via the Redlich–kwong equation of state and the Soave modification
of Redlich-kwong.

5. GENERAL FORM OF EQUATION
 For a given amount of substance contained in a system, the temperature, volume, and
pressure are not independent quantities; they are connected by a relationship of the
general form
 f(P, V ,T)=0An equation used to model this relationship is called an equation of state. In
the following sections major equations of state are described, and the variables used here
are defined as follows. Any consistent set of units may be used, although SI units are
preferred. Absolute temperature refers to use of the Kelvin (K) or Rankine (°R)
temperature scales, with zero being absolute zero.
 , pressure (absolute)
 , volume
 , number of moles of a substance
 Vm, V∕ȵ, molar volume, the volume of 1 mole of gas or liquid
 T, absolute temperature
 R, ideal gas constant ≈ 8.3144621 J/mol·K
 Pc, pressure at the critical point
 V, molar volume at the critical point
 C, absolute temperature at the critical point

6.  The classical ideal gas law may be written
 PV=nRT.
 In the form shown above, the equation of state is thus
 f(p,V,T)=pV-nRT=0.
 If the calorically perfect gas approximation is used, then the
ideal gas law may also be expressed as follows
 P=ᵨ(ϒ-1)ҽ
 Where ᵨ is the density, ϒ =Cp/Cv is the adiabatic index (ratio of
specific heats), ҽ=Cv T is the internal energy per unit mass (the
"specific internal energy"), Cv is the specific heat at constant
volume, and Cv is the specific heat at constant pressure.

10. Beattie-Bridgeman Equation of State:
The Beattie-Bridgeman equation of state was proposed in 1928. It has five experimentally
determined constants.
Per unit mass Per unit mole
v (m3/kg) (m3/kmol)
u (kJ/kg) (kJ/kmol)
h (kJ/kg) (kJ/kmol)
Properties Per Mass and Per Mole
The properties with a bar on top are molar basis.
The five constants can be found in the table below where P is in kPa, is in m3/kmol, T is in
K and Ru is equal to 8.314 (kPa-m3) / (Kmol-K). The Beattie-Bridgeman equation of state is
valid when ρ < 0.8 ρcr (critical density).

17. Virial Equation of State
• Although usually not the most convenient equation of state, the
virial equation is important because it can be derived directly
from statistical mechanics. This equation is also called
the Kamerlingh Onnes equation. If appropriate assumptions are
made about the mathematical form of intermolecular forces,
theoretical expressions can be developed for each of
the coefficients. A is the first virial coefficient, which has a
constant value of 1 and makes the statement that when volume
is large, all fluids behave like ideal gases. The second virial
coefficient B corresponds to interactions between pairs of
molecules, C to triplets, and so on. Accuracy can be increased
indefinitely by considering higher order terms. The
coefficients B, C, D, etc. are functions of temperature only.

18.  One of the most accurate equations of state is that from
Benedict-Webb-Rubin-Starling shown next. It was very
close to a virial equation of state. If the exponential term in
it is expanded to two Taylor terms, a virial equation can be
derived:
• Note that in this virial equation, the fourth and fifth virial
terms are zero. The second virial coefficient is
monotonically decreasing as temperature is lowered. The
third virial coefficient is monotonically increasing as
temperature is lowered.