PROPERTIES OF A PURE
SUBSTANCE
MEC121
LECTURE 2
Pure substance: a material with
homogeneous and invariable
composition.
• Pure substances can have multiple phases: an
ice-water mixture is still a pure substance.
• An air-steam mixture is not a pure substance.
• Air, being composed of a mixture of N2, O2, and
other gases, is formally not a pure substance. But
can often treat air as a pure substance
with little error.
Temperature − Specific Volume
Temperature − Specific Volume
Above a critical pressure,
P = Pc = 22.089 MPa, there is no
phase change observed!1 At the
critical pressure,
the temperature takes on a critical
temperature of
Tc = 374.14 ◦C.
At the critical pressure and
temperature, the specific volume
takes the
value
vf = vg = vc = 0.003155 m3/kg.
saturated liquid: the material is at Tsat and is all liquid.
saturated vapor: the material is at Tsat and is all vapor.
compressed (subcooled) liquid: the material is liquid with T < Tsat.
superheated vapor: the material is vapor with T > Tsat.
two-phase mixture: the material is composed of co-existing liquid
and vapor with
both at Tsat
Quality (x)
• quality= x: as the ratio of
the mass of the mixture that
is vapor (vap) to the total
mixture mass:
x = mvap/mtotal
.
x = 0: corresponds
to mvap = 0. This is the all
liquid limit.
x = 1: corresponds
to mvap = mtotal. This is the
all gas limit.
x ∈ [0, 1].
Independent properties
• Simple compressible substance: a material that can be worked upon by
pressure forces.
For a simple compressible substance, two independent intensive
thermodynamic properties define the state of the system.
superheated vapor /compressed(subcooled) liquid:
P = P(T, v),
v = v(T, P),
or T = T(P, v).
two-phase mixture: If we have a two-phase mixture, our
experiments show that P and T are not independent. In this case,
we need another property to characterize the system. That
property is the quality, x. So for two-phase mixtures, we might have
v = v(T, x), for example.
• Thermal equation of state: an equation that gives the pressure as a
function of two independent state variables. An example is the general
form:
Saturated Table (water)
Compressed Liquid Table
Superheated Table
Linear interpolation
• Interpolation is often required when exact values are
not tabulated.
• primarily use linear interpolations.
• Use extrapolations only if there is no other choice.
• Occasionally double interpolations will be necessary.
Interpolation
Thermodynamic Surfaces
Ideal gas
• Ideal gas law: This equation, which is a
combination of Boyle’s law, Charles’ law, and
Avogadro’s law, is most fundamentally stated
as
P V = nṜT
Ideal Gas
• Ř is independent of material (universal gas
constant).
• M; molecular weight of gas,
• R ; gas constant of a particular gas.
Compressibility factor
Ideal Gas
Example: Given air in a cylinder with stops and a frictionless piston with area A =
0.2 m2 , stop height of 1 m, and total height of 2 m, at initial state P1 = 200 kPa
and T1 = 500 ◦C with cooling, find 1. the temperature when the piston reaches the
stops, and •2. the pressure if the cooling continues to T = 20 ◦C.
three distinct states:
• state 1: initial state
•state 2: piston reaches the stops
• state 3: final state, where T = 20◦C.
Ideal Gas
Ideal Gas