Using Property Charts of Water

When solving thermodynamic problems involving
water, we rely on the state properties to calculate changes. Let’s see how we can
use water property charts to acquire state properties. Let us get familiar with a temperature-entropy
chart for water. With this we plot the constant pressure lines, isobars, the constant specific
volume lines, the isochors and finally the constant enthalpy lines. We understand that
we can use these charts to acquire state properties, say within the saturated or the superheated
region. Of course, we need a more detailed chart to solve common thermodynamic problems
in the textbook. So let us build one. A detailed T-s Property Chart has numerous
constant property lines that we can use to retrieve thermodynamic properties of water.
We begin with our axes, Entropy s on the x-axis and Temperature T in Celsius on the y-axis. We first plot the isobars in Mega-Pascals.
Because the phase change process happens at a constant temperature, we can eliminate these
isobars within the dome – just to reduce clutter. Instead, let us bound this area with the Saturated
Liquid line to the left and the Saturated Vapor line to the right. In between, we can
populate the mixture dome with constant quality lines going from 0% to 100% vapor. Densities are plotted only in the Superheated
region – and not in the saturated region to avoid confusion. Also, notice that these do
not increase arithmetically – they are multiples of 3 and 3-and-a-third. More on this later.
Finally we add constant enthalpy lines to complete our T-s Property Chart. This T-s property chart can be divided into
multiple regions. First we have our compressed liquid region. Here pressure does not have
much of an effect on properties. Then we have the Saturated region, where we have mixture
of liquid and vapor-phase of water defined by quality x. The Supercritical region is
above the critical temperature 374 oC and pressure of 22 MPa. And finally the Superheated
region to the right where water begins to behave like an ideal gas. Let us practice retrieving properties from
different regions. For this we are going to pick a constant pressure of 2 atmospheres,
that’s about 200 kPa. We begin at 500 oC. This state is in the superheated region. Collect
the easiest properties first. The enthalpy value on the green line and the entropy on
the x-axis. The Specific Volume requires an extra step
because the sequence of density lines is geometric rather an arithmetic sequence with a common
difference. First we understand that specific volume is the inverse of density. Next we
must identify the two lines that bound our state and calculate the ratio – 3-and-a-third,
in this case. Then the density of our state is the lower density times the ratio of the
two densities raised to the power that is the fractional distance from lower reference
to our state. Here our state is about half way between and hence we raise it to the power
of a half. This gives us a density of 0.55 kg/m3; which when inverted gives us a specific
volume of 1.8 m3/kg. Internal Energy is not plotted on a T-s chart
but we know that internal energy u is a function of enthalpy, pressure, and the specific volume.
So we plug those values in and arrive at our internal energy of the state. At this point,
we have retrieved all the properties required for this superheated state. Next, let us use our water at 200 kPa but
cool the water to partially condense it to get a mixture quality of 60%. Again, there
are state properties that are easy to read off: the Saturation temperature is 120 oC,
the Enthalpy, and the Entropy are good starting points. The Specific Volume within the saturated region
is bounded by the saturated liquid value to the left and the saturated vapor value to
the right. At the saturated liquid line, specific volume is 0.001 m3/kg – the inverse of 1000
kg/m3 for liquid water. The value to the right needs to be computed, like before. That state
is bounded by two constant density lines with a ratio of 3. Here our state is about tenth
of the way to the next line. Using a similar approach as before, we get the vapor phase
specific volume. However, our state is only 60% vapor. For this we are not going to worry
about liquid phase and simply take the 60% of that vapor phase value. Internal energy is straightforward now because
you have all the needed values. So plug these in and get your internal energy. We are done
retrieving all the properties for our mixture state. We are going to keep cooling this mixture,
at 200 kPa, until we only have liquid water at a temperature of 50 oC. Liquids are considered
incompressible because they do not change their properties with pressure. Therefore,
we can safely assume that the properties of a liquid can be estimated using the saturated
liquid properties at the same temperature. So we move over to the right and read off
our state properties on the saturated liquid line at 50 oC. The specific volume is simply
0.001 m3/kg; and because of this small specific volume the internal energy and the enthalpy
are nominally the same. Again, we have all the properties for this state. This way the property charts are very useful
for quickly retrieving property values. Additionally, they provide a realistic depiction of a steam
power cycle. A power cycle is used to generate electricity and the simplest one is composed
of four states. We first pump liquid water from State 1 to 2 – with only a minor change
in location on the chart. Next, we use a boiler to heat the liquid water to a superheated
state 3. This superheated state is then fed into a turbine where we extract the energy
to drive an electrical generator. Finally we use a condenser to bring the state back
to where we started. We can now use this cycle to predict the performance of our power station.
This is a very simple cycle but you can already see the benefits of using property charts.