THERMODYNAMICS  THEORY



For most substances,
thermodynamic properties are presented in the form of tables because
they are too complex to be expressed by simple equations.
In thermosystems, many working fluids can be used. Water is one of
the most common working fluids involved. It is the only liquid
presented
in this
section.
The thermodynamic properties that are commonly used are:
 Temperature (T), ^{o}C or ^{o}F
 Pressure (P), Pa or psia
 Specific volume (v) (the volume per unit mass), m^{3}/kg or
ft^{3}/lb
 Specific internal energy (u), kJ/kg or Btu/lb
 Specific enthalpy (h), kJ/kg or Btu/lb
 Specific entropy (s) (Which will be introduced in the following section),
kJ/(kgK) or Btu/(lbR)






Saturated Liquid and Saturated Vapor

Saturated Water Table
Saturated Water Temperature Table
Saturated Water Pressure Table


At a given pressure, the temperature at which a pure
substance changes phase is called the saturation temperature. At 1 atm,
the saturation temperature of water is 100 ^{o}C. At a given
temperature, the pressure at which a pure substance changes phase is
called the saturation
pressure. At 100 ^{o}C, the saturation
pressure of water is 1 atm. The saturation temperature and saturation
pressure depends on each other.
There are two types of tables for saturated water. Both tables give
the same information. The only difference is that the properties are
listed either as a function of temperature or pressure.
The properties listed in the tables include
 Saturation pressure (P_{sat}) for a given temperature or
saturation temperature (T_{sat}) for a given pressure
 Specific volume of saturated liquid (v_{f}) and saturated
vapor (v_{g})
 Specific internal energy of saturated liquid (u_{f}),
saturated vapor (u_{g}), and vaporization (u_{fg} =
u_{g}  u_{f})
 Specific enthalpy of saturated liquid (h_{f}), saturated
vapor (h_{g}), and vaporization (h_{fg} = h_{g} 
h_{f}) or latent heat of vaporization.
 Specific entropy of saturated liquid (s_{f}), saturated
vapor (s_{g}), and vaporization (s_{fg} = s_{g} 
s_{f})






Saturated Mixture



During the vaporization process of water, the substance is a mixture
of saturated liquid and saturated vapor. Quality (x) is defined to describe
the fraction of saturated vapor in the mixture.
x = m_{vapor}/m_{total}
where m_{vapor} = mass of
vapor in the mixture
m_{total} = total mass of the mixture
m_{total} = m_{liquid} +
m_{vapor} = m_{f} + m_{g}
Quality has a value between 0 and 1. x equals 1 for saturated
vapor and x equals 0 for saturated liquid according
to
its
definition.
Saturated mixture is a twophase system. For convenience, it can be
treated as a homogenous mixture and the properties of this mixture is
simply the average properties of the saturated liquid and saturated
vapor. For example, the specific volume of the mixture can be determined
by




Quality is related to the horizontal distance on Tv diagram 

V_{av} = V_{f} +
V_{g
} m_{total} v_{av} =
m_{f} v_{f} + m_{g} v_{g
} v_{av} = m_{f} v_{f}/m_{total} +
m_{g} v_{g}/m_{total}
= v_{f} (1
 m_{g}/m_{total}) + v_{g } m_{g}/m_{total}
= v_{f} (1
 x_{}) + v_{g} x
= v_{f} +
v_{fg} x
Rearranging the above equation to give an expression for the quality
x as
x = (v_{av}  v_{f})/v_{fg}
Based on this equation, quality can be determined from the horizontal
distance on the Tv or Pv diagram as shown in the figure.
The above process can be repeated for u and h.
u_{av} = u_{f} +
u_{fg} x
h_{av} = h_{f} + h_{fg} x 





Superheated Vapor

Superheated Water Table
Superheated Steam Table


Since the superheated vapor is a single phase substance,
the temperature and pressure are independent. In the superheated vapor
tables, the properties are listed as a function of both the temperature
and pressure. The tabulated properties include v, u, h and s. The saturation
temperature corresponding
to the
pressure
is given in the parentheses following the pressure value.
Superheated vapor can be characterized by
 P < P_{sat }at a given T
 T > T_{sat }at a given P
 v > v_{g }at a given P or T
 u > u_{g }at a given P or T
 h > h_{g }at a given P or T






Subcooled Liquid

Subcooled Water Table


The format of the subcooled liquid water
tables is similar to the format of the superheated vapor tables.
In the absence of compressed liquid data, a common practice is to use the saturated
liquid data based on the given temperature to estimate the properties
of compressed liquid. For h, the error can be reduced using the following approximation
Subcooled liquid can be characterized by
 P > P_{sat }at a given T
 T < T_{sat }at a given P
 v < v_{f }at a given P or T
 u < u_{f }at a given P or T
 h < h_{f }at a given P or T



