3.4 Property of a Two phase Mixture/Quality
During a vaporization process, a substance exists as part liquid and part vapor. That is, it is a
mixture of saturated liquid and saturated vapor(Fig. 3–34). 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 thetotal mass
of the mixture:
where,
Quality has significance for saturated mixtures only. It has no meaning inthe compressed liquid
or superheated vapor regions. Its value is between 0 and 1. The quality of a system that
consists of saturated liquid is 0 (or 0 percent), and the quality of a system consisting of
saturated vapor is 1 (or 100 percent).
Consider a tank that contains a saturated liquid–vapor mixture. The volume occupied by
saturated liquid is Vl
, and the volume occupied by saturated vapor is Vg. The total volume V is
the sum of the two:
where, is defined as the difference between
the specific volumes of the saturated vapor and
the saturated liquid i.e. .
Any intensive property such as h,u,s can be evaluated for a state in the saturated/wet region
by relating it with quality (x) i.e. for any intensive property 'z', we can write.
3.5 Other Thermodynamic Properties
3.5.1. Enthalpy: A combine property
In the analysis of certain types of processes, particularly in power generation and refrigeration,
we frequently encounter the combination of properties u+PV. For the sake of simplicity and
convenience, this combination is defined as a new property, enthalpy, and denoted by 'h'
h=u+Pv (kJ/kg)
H=U+PV (kJ)
3.5.2 Specific Heat
The specific heat is defined as the energy required to
raise the temperature of a unit mass of a substance by
one degree. In thermodynamics, we are interested in two
kinds of specific heats: specific heat at constant volume
cv and specific heat at constant pressure cp.
Physically, the specific heat at constant volume cv can be
viewed as the energy required to raise the temperature
of the unit mass of a substance by one degree as the
volume is maintained constant. The energy required to
do the same as the pressure is maintained constant is the specific heat at constant pressure cp.
The specific heat at constant pressure cp is always greater than cv because at constant pressure
the system is allowed to expand and the energy for this expansion work must also be supplied
to the system.
In thermodynamics, specific heat at constant volume cv is defined as the change in the
internal energy of a substance per unit change in temperature at constant volume.
Likewise, specific heat at constant pressure cp can be defined as the change in the enthalpy of a
substance per unit change in temperature at constant pressure.
In other words, cv is a measure of the variation of internal energy of a substance with
temperature, and cp is a measure of the variation of enthalpy of a substance with
temperature. Thus, change in internal energy and enthalpy can be written.
The important characteristic of a pure substance is that it is invariable in chemical composition
even though there may be a change of phase. Thus, a system consisting of a mixture of various
phases of water viz. water and ice, water and steam is a pure substance. Similes rly, a system
consisting of oxygen as a vapor; a liquid or a combination of these is also a pure substance. Air,
however, though a mixture of several gases is considered as a pure substance only as long as it
is all gas or all liquid. A mixture of dry gaseous air and liquid air is not a pure substance,
because chemical composition of liquid phase is different from that of vapor phase.
State Postulates
The number of properties required to fix the state of a system is given by the state postulate
and is defined as the general rule that is developed as a guide in determining the number of
independent properties required to fix the state of a system.
For a pure simple compressible substance, repeated observations and experiments show that
two independent properties are necessary and sufficient to establish the stable equilibrium
state of a system. The word simple and compressible imply that the only work mode
considered is the PdV work form. A system is called a simple compressible system in the
absence of electrical, magnetic, gravitational, motion, and surface tension effects.
The observed behavior of a pure simple compressible substance is summarized in the state
postulates:
The values of any two independent thermodynamic properties are sufficient to establish the
stable thermodynamic state of a pure simple compressible substance.
If T and v are known for a pure compressible substance, then P and u have unique known
values. Mathematically this is given as
P=P(T,v) and u=u(T,v)
3.2 Ideal Gas
A perfect gas or an ideal gas is defined as a gas having no forces of molecular attraction. A gas
which follows the gas laws at all ranges of pressures and temperatures can be considered as an
ideal gas but no such gas exists in nature. However, real gases tend to follow these laws at low
pressures or high temperatures or at both. This is because the molecules are far apart at
reduced pressures and elevated temperatures and the force of attraction between them tends
to be small. At low pressures, the gases behave nearly as ideal gases. The range of this low
pressure is different for different gases.
3.2.1 Boyle's Law
This law was enunciated by Robert Boyle in 1661 on the basis of his experimental results.
Homogeneous in chemical compostion means that the chemical elements must be combined
chemically in the same way in all parts of the system. Consideration of Figure 3.1 shows that
system (i) satisfies this condition also; for steam and water consists of identical
molecules. System (ii) on the other hand is not homogeneous in chemical aggregation
since, in the upper part of the system, the hydrogen and oxygen are not combined
chemically (individual atoms of H and O are not uniquely associated), whereas in the lower part
of the system the he hydrogen and oxygen are combined in the form of water.
During a vaporization process, a substance exists as part liquid and part vapor. That is, it is a
mixture of saturated liquid and saturated vapor(Fig. 3–34). 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 thetotal mass
of the mixture:
where,
Quality has significance for saturated mixtures only. It has no meaning inthe compressed liquid
or superheated vapor regions. Its value is between 0 and 1. The quality of a system that
consists of saturated liquid is 0 (or 0 percent), and the quality of a system consisting of
saturated vapor is 1 (or 100 percent).
Consider a tank that contains a saturated liquid–vapor mixture. The volume occupied by
saturated liquid is Vl
, and the volume occupied by saturated vapor is Vg. The total volume V is
the sum of the two:
where, is defined as the difference between
the specific volumes of the saturated vapor and
the saturated liquid i.e. .
Any intensive property such as h,u,s can be evaluated for a state in the saturated/wet region
by relating it with quality (x) i.e. for any intensive property 'z', we can write.
3.5 Other Thermodynamic Properties
3.5.1. Enthalpy: A combine property
In the analysis of certain types of processes, particularly in power generation and refrigeration,
we frequently encounter the combination of properties u+PV. For the sake of simplicity and
convenience, this combination is defined as a new property, enthalpy, and denoted by 'h'
h=u+Pv (kJ/kg)
H=U+PV (kJ)
3.5.2 Specific Heat
The specific heat is defined as the energy required to
raise the temperature of a unit mass of a substance by
one degree. In thermodynamics, we are interested in two
kinds of specific heats: specific heat at constant volume
cv and specific heat at constant pressure cp.
Physically, the specific heat at constant volume cv can be
viewed as the energy required to raise the temperature
of the unit mass of a substance by one degree as the
volume is maintained constant. The energy required to
do the same as the pressure is maintained constant is the specific heat at constant pressure cp.
The specific heat at constant pressure cp is always greater than cv because at constant pressure
the system is allowed to expand and the energy for this expansion work must also be supplied
to the system.
In thermodynamics, specific heat at constant volume cv is defined as the change in the
internal energy of a substance per unit change in temperature at constant volume.
Likewise, specific heat at constant pressure cp can be defined as the change in the enthalpy of a
substance per unit change in temperature at constant pressure.
In other words, cv is a measure of the variation of internal energy of a substance with
temperature, and cp is a measure of the variation of enthalpy of a substance with
temperature. Thus, change in internal energy and enthalpy can be written.
The important characteristic of a pure substance is that it is invariable in chemical composition
even though there may be a change of phase. Thus, a system consisting of a mixture of various
phases of water viz. water and ice, water and steam is a pure substance. Similes rly, a system
consisting of oxygen as a vapor; a liquid or a combination of these is also a pure substance. Air,
however, though a mixture of several gases is considered as a pure substance only as long as it
is all gas or all liquid. A mixture of dry gaseous air and liquid air is not a pure substance,
because chemical composition of liquid phase is different from that of vapor phase.
State Postulates
The number of properties required to fix the state of a system is given by the state postulate
and is defined as the general rule that is developed as a guide in determining the number of
independent properties required to fix the state of a system.
For a pure simple compressible substance, repeated observations and experiments show that
two independent properties are necessary and sufficient to establish the stable equilibrium
state of a system. The word simple and compressible imply that the only work mode
considered is the PdV work form. A system is called a simple compressible system in the
absence of electrical, magnetic, gravitational, motion, and surface tension effects.
The observed behavior of a pure simple compressible substance is summarized in the state
postulates:
The values of any two independent thermodynamic properties are sufficient to establish the
stable thermodynamic state of a pure simple compressible substance.
If T and v are known for a pure compressible substance, then P and u have unique known
values. Mathematically this is given as
P=P(T,v) and u=u(T,v)
3.2 Ideal Gas
A perfect gas or an ideal gas is defined as a gas having no forces of molecular attraction. A gas
which follows the gas laws at all ranges of pressures and temperatures can be considered as an
ideal gas but no such gas exists in nature. However, real gases tend to follow these laws at low
pressures or high temperatures or at both. This is because the molecules are far apart at
reduced pressures and elevated temperatures and the force of attraction between them tends
to be small. At low pressures, the gases behave nearly as ideal gases. The range of this low
pressure is different for different gases.
3.2.1 Boyle's Law
This law was enunciated by Robert Boyle in 1661 on the basis of his experimental results.
Homogeneous in chemical compostion means that the chemical elements must be combined
chemically in the same way in all parts of the system. Consideration of Figure 3.1 shows that
system (i) satisfies this condition also; for steam and water consists of identical
molecules. System (ii) on the other hand is not homogeneous in chemical aggregation
since, in the upper part of the system, the hydrogen and oxygen are not combined
chemically (individual atoms of H and O are not uniquely associated), whereas in the lower part
of the system the he hydrogen and oxygen are combined in the form of water.