[BASIC THERMODYNAMICS] Pure substances

A substance that has a fixed chemical composition throughout is called a pure substance.
Water, nitrogen, helium, and carbon dioxide, for example, are all pure substances.

A mixture of various chemical elements or compounds also

qualifies as a pure substance as long as the mixture is
homogeneous. Air, for example, is a mixture of several gases, but
it is often considered to be a pure substance because it has a
uniform chemical composition (Fig. 3–1). However, a mixture of
oil and water is not a pure substance. Since oil is not soluble in
water, it will collect on top of the water, forming two chemically
dissimilar regions.

A mixture of two or more phases of a pure substance is still a

pure substance as long as the chemical composition of all phases
is the same (Fig. 3–2). A mixture of ice and liquid water, for
example, is a pure substance because both phases have the same
chemical composition. A mixture of liquid air and gaseous air,
however, is not a pure substance since the composition of liquid
air is different from the composition of gaseous air, and thus the
mixture is no longer chemically homogeneous. This is due to
different components in air condensing at different temperatures
at a specified pressure.

Phases of pure substance:

A material can exist in the
1. solid phase
2. liquid phase
3. vapor (gas) phase
4. a mixture of the phases at equilibrium, e.g., melting, vaporization or sublimation.

Compressed Liquid and Saturated Liquid: (just try to realize the facts. No need to memorize for Exam)

Consider a piston–cylinder device containing liquid water at 20°C and 1 atm

pressure (state 1, Fig. 3–6). Under these conditions, water exists in the liquid phase,
and it is called a compressed liquid, or a subcooled liquid, meaning that it is not
about to vaporize. Heat is now transferred to the water until its temperature rises to,
say, 40°C. As the temperature rises, the liquid water expands slightly, and so its
specific volume increases. To accommodate this expansion, the piston moves up
slightly. The pressure in the cylinder remains constant at 1 atm during this process
since it depends on the outside barometric pressure and the weight of the piston,
both of which are constant. Water is still a compressed liquid at this state since it has
not started to vaporize.

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 [BASIC THERMODYNAMICS] Pure substances

As more heat is transferred, the temperature keeps rising until it reaches

100°C (state 2, Fig. 3–7). At this point water is still a liquid, but any heat
addition will cause some of the liquid to vaporize. That is, a phase-change
process from liquid to vapor is about to take place. A liquid that is about to
vaporize is called a saturated liquid. Therefore, state 2 is a saturated liquid
state.

Saturated Vapor and Superheated Vapor: (just try to realize the facts. No need to memorize for Exam)
Once boiling starts, the temperature stops rising until the liquid is
completely vaporized. That is, the temperature will remain constant
during the entire phase-change process if the pressure is held constant.
This can easily be verified by placing a thermometer into boiling pure
water on top of a stove. At sea level (P = 1 atm), the thermometer will
always read 100°C if the pan is uncovered or covered with a light lid.
During a boiling process, the only change we will observe is a large
increase in the volume and a steady decline in the liquid level as a result
of more liquid turning to vapor.
Midway about the vaporization line (state 3, Fig. 3–8), the cylinder
contains equal amounts of liquid and vapor. As we continue transferring
heat, the vaporization process continues until the last drop of liquid is
vaporized (state 4, Fig. 3–9). At this point, the entire cylinder is filled with
vapor that is on the borderline of the liquid phase. Any heat loss from this
vapor will cause some of the vapor to condense (phase change from vapor
to liquid). A vapor that is about to condense is called a saturated vapor.
Therefore, state 4 is a saturated vapor state. A substance at states between
2 and 4 is referred to as a saturated liquid–vapor mixture since the
liquid and vapor phases coexist in equilibrium at these states.

Once the phase-change process is completed, we are back to a single

phase region again (this time vapor), and further transfer of heat results in
an increase in both the temperature and the specific volume (Fig. 3–10).
At state 5, the temperature of the vapor is, let us say, 300°C; and if we
transfer some heat from the vapor, the temperature may drop somewhat
but no condensation will take place as long as the temperature remains
above 100°C (for P = 1 atm). A vapor that is not about to condense (i.e.,
not a saturated vapor) is called a superheated vapor. Therefore, water at
state 5 is a superheated vapor.

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 [BASIC THERMODYNAMICS] Pure substances

T-V diagram for constant Pressure (isobaric) Phase-change process:

1 2 2 4 4 5

If the entire process described here is

reversed by cooling the water while
maintaining the pressure at the same
value, the water will go back to state
1, retracing the same path, and in so
doing, the amount of heat released
will exactly match the amount of
heat added during the heating
process.

Saturation Temperature and Saturation Pressure: (just try to realize the facts. No need to memorize for Exam)
It probably came as no surprise to you that water started to boil at 100°C. Strictly speaking, the statement
“water boils at 100°C” is incorrect. The correct statement is “water boils at 100°C at 1 atm pressure.” The
only reason water started boiling at 100°C was because we held the pressure constant at 1 atm (101.325
kPa). If the pressure inside the cylinder were raised to 500 kPa by adding weights on top of the piston,

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 [BASIC THERMODYNAMICS] Pure substances

water would start boiling at 151.8°C. That is, the temperature at which water starts boiling depends on
the pressure; therefore, if the pressure is fixed, so is the boiling temperature.
At a given pressure, the temperature at which a pure substance changes phase is called the saturation
temperature Tsat. Likewise, at a given temperature, the pressure at which a pure substance changes phase
is called the saturation pressure Psat. At a pressure of 101.325 kPa, Tsat is 99.97°C. Conversely, at a
temperature of 99.97°C, Psat is 101.325 kPa.

PROPERTY DIAGRAMS FOR PHASE-CHANGE PROCESSES:

T-v diagram:

As the pressure is increased further, this saturation line continues to shrink, as shown in Fig., and it
becomes a point when the pressure reaches 22.06 MPa for the case of water. This point is called the
critical point, and it is defined as the point at which the saturated liquid and saturated vapor states are
identical.
The temperature, pressure, and specific volume of a substance at the critical point are called, respectively,
the critical temperature Tcr , critical pressure Pcr, and critical specific volume vcr. The critical-point
properties of water are Pcr = 22.06 MPa, Tcr = 373.95°C, and vcr = 0.003106 m/kg.

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 [BASIC THERMODYNAMICS] Pure substances

Above the critical state, there is no line that separates the compressed liquid region and the superheated
vapor region. However, it is customary to refer to the substance as superheated vapor at temperatures
above the critical temperature and as compressed liquid at temperatures below the critical temperature.

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 [BASIC THERMODYNAMICS] Pure substances

The P-v Diagram:

The general shape of the P-v diagram of a pure substance is very much like the T-v diagram, but the T _
constant lines on this diagram have a downward trend, as shown in Fig.

Vapor Quality:

At point A subcooled/compressed liquid, at point B superheated condition.

Between points L and V you have a mixture of liquid and vapor at equilibrium.

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 [BASIC THERMODYNAMICS] Pure substances

To analyze this mixture properly, we need to know the proportions of the liquid and vapor phases in the
mixture. This is done by defining a new property called the quality x as the ratio of the mass of vapor to
the total mass of the mixture:

Quality has significance for saturated mixtures only. It has no meaning in the compressed liquid or
superheated vapor regions. Its value is between 0 and 1.
at point L  x = 0
at point V  x = 1

All results are of same format can be summarized by a single

equation:
yavg = yf + xyfg
For simplicity, y = yf + xyfg

This equation is used for internal energy, enthalpy & entropy.

u = uf + xufg h = hf + xhfg s = sf + xsfg

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 [BASIC THERMODYNAMICS] Pure substances

Example:
A cylinder-piston assembly initially contains water at 3 MPa and 300 oC. The water
is cooled at constant volume to 200 oC, then compressed isothermally to a final
pressure of 2.5 MPa. Sketch the process on a T-v diagram and find the specific
volume at the 3 states.

State 1 State 2 State 3

3 MPa Cool at Compress

o
2.5 MPa
300oC Constant V 200 C isothermally

3 MPa
T
2.5 MPa
300oC 1

Tsat(3 MPa)
P2

Tsat(2.5 MPa)

3
200oC
2

State 1:
From the saturated water (liquid-vapor) table A-3:
3MPa (30 bar) Tsat= 233.9oC
since T1 > 233.9oC  superheated vapor

From the superheated water vapor table A-4:

3MPa and 300oC v1= 0.0811 m3/kg

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 [BASIC THERMODYNAMICS] Pure substances

State 2:
Cooled at constant volume, so v2= v1= 0.0811 m3/kg
From the saturated water (liquid-vapor) table A-2:
200oC vf= .001157m3/kg, vg= .1274 m3/kg
because vf < v2< vg we have a liquid vapor mixture

recall, v = vf + x vfg

= vf + x (vg – vf)

v2= v1= 0.0811 = .0001157 + x (.1279 - .0001157)

x = 0.633 i.e., 63.3% vapor by mass

State 3:
Compressed isothermally to 2.5 MPa, so T3 = T2 = 200oC
From table A-3 for 2.5 Mpa (25 bar) Tsat= 224oC
As T2= 200oC < Tsat  compressed liquid

From the compressed liquid water table A-5:

200oC and 2.5 MPa  v3= 1.155x10-3 m3/kg

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 [BASIC THERMODYNAMICS] Pure substances

The T-s diagram and h-s (Molier diagram) of pure substances shows following natures:

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