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# Tables of thermodynamic properties

Tables of thermodynamic properties of many substances
are available, and  in  general, all
these have same form.

Steam tables are selected because
steam is used extensively in power plants and industrial processes.

The steam tables provide the data of useful
thermodynamic properties like T, P,  v, u, h and s  for saturated liquid, saturated vapor and
superheated vapor.

Since the properties like internal
energy, enthalpy and entropy of a system cannot be directly measured; they are
related to change in the energy of the system.

Hence one can determine ∆u, ∆h, ∆s, but not the absolute
values  of  these
properties.  Therefore it is
necessary to choose a reference state to which these properties are arbitrarily
assigned some numerical values.

For water, the triple point (T = 0.01o
C and P = 0.6113 kPa) is selected as the reference state, where the internal
energy and entropy of saturated liquid are assigned a zero value.

In the saturated steam tables, the properties of
saturated liquid that is in equilibrium with saturated vapor are presented.

During phase transition, the pressure
and temperature are not independent of
each other.  If  the temperature is specified, the pressure at
which both phases coexist in equilibrium is equal   to the saturation pressure.

Hence, it is possible to choose either temperature or
pressure as the independent variable, to specify the state of two-phase system.

Depending on whether the temperature or pressure is used
as the independent variable, the tables are called temperature or pressure tables.

The two phases- liquid and vapor can
coexist in a state of equilibrium only up to the critical point.

Therefore the listing of the
thermodynamic properties of steam in the saturated steam tables ends at the
critical point (374.15o C and 212.2 bar).

If the steam exists in only one phase (superheated
steam), it is necessary to specify two independent  variables, pressure and temperature, for the
complete specification  of the
state.   In the superheated steam tables,
the properties- v, u, h, and s- are
tabulated  from  the
saturation temperature to some temperature for a given pressure.

The thermodynamic properties of a liquid and vapor
mixture can be evaluated in terms of its quality. In particular, the specific
volume, specific internal energy, specific enthalpy and specific entropy of a
mixture of quality X are given by

v = (1-X)vf + Xvg,

u = (1-X)uf
+ Xug,

h = (1-X)hf + Xhg = hf + Xhfg

s = (1-X)sf + Xhg

where hfg = hg
hf = latent hat of vaporization.

### Temperature-volume diagram

The locus of all the saturated states gives the saturated liquid curve
AC and the  locus of  all the saturated vapor states gives the
saturated vapor states gives the
saturated  vapor  states
gives the saturated vapor curve BC.

The point C represents the critical point. The difference between vg
and vf reduces as the pressure is increased, and at the critical
point vg = vf .

At the critical point, the
two phases-liquid and vapor- are indistinguishable.

### Pressure-volume diagram

The
pressure-volume (P-V) diagram for a pure substance is shown in Figure. The
curves AC and BC represent the
saturated liquid curve and saturated vapor curve, respectively, and C is
critical point.

The area under the curve represents the two-phase region. Any point M in
this region is a mixture of saturated liquid (shown as f) and saturated vapor
(g).

### Mollier (h-s) Diagram

The h-s diagram was introduced by
Richard Mollier and was named after him.

It consists of a family of
constant pressure lines, constant temperature lines and constant volume lines
plotted on enthalpy versus entropy coordinates.

In the two-phase region, the constant
pressure and constant temperature lines coincide.

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