### Steam P-H Diagram

The pressure enthalpy diagram for steam is an excellent tool to gain an understanding of the steam tables. The pressure-enthalpy diagram describes the liquid, vapor and mix region of water. As shown in the following figure, the P-H diagram consists of Pressure (PSIA) on the y-axis and Enthalpy (Btu/lbm) on the x-axis. It is important to note that pressure is shown on a logarithmic scale while enthalpy is shown in a normal scale. In the middle of the diagram is the vapor dome. This dome separates the sub-cooled liquid (aka water) on the left side, super-heated vapor (aka steam) on the right side and the liquid-vapor mix region (aka mixed region or wet region) in the middle.

The mixed region is cut by upward sloping lines that represent the percentage of vapor, as shown in the following figure. The figure shows that as you move from left to right on a constant pressure line, the percentage of vapor increases from 0% at the saturated liquid to 100% at the saturated vapor line. The percentage of vapor is also known in other terms as steam quality and dryness fraction, where saturated vapor has a steam quality or dryness fraction of 1.

The P-H diagram is also helpful in illustrating the relationship between the enthalpy of the saturated liquid, saturated vapor and the enthalpy of vaporization.

As shown on the following figure, on the left the enthalpy of saturated liquid is found and as enthalpy is added to the saturated liquid, moving from left to right at constant pressure, the enthalpy of saturated gas (steam) is found at the saturated vapor line. The difference between the two enthalpies is the latent heat (enthalpy) of vaporization.

If a point in the mix region is selected, then the relationship between the enthalpy of the mixed steam and the enthalpy of saturated liquid, enthalpy of vaporization and steam quality is as shown below.

In the figure above, the point is shown on the 50% steam quality, therefore only 50% of the enthalpy of vaporization has been added to the enthalpy of saturated liquid.

The next important part of the P-H diagram is the constant temperature lines. These lines are characterized by nearly vertical lines in the sub-cooled liquid and super-heated steam region. This means that any increase in enthalpy during these phases, causes the temperature of the liquid or steam to increase and vice versa for decreases in enthalpy. in the mixed region, temperatures are shown to remain constant with increasing enthalpy and are identified as horizontal lines. As enthalpy is added to a saturated liquid, the temperature does not change, because the enthalpy is going towards the enthalpy of vaporization and is changing the phase of the liquid to a vapor.

A common point on the P-H diagram that the engineer should memorize is the location of the boiling point of water at 1 atmosphere (14.7 PSIA) which is 212 F. It is important to note that if the temperature of a saturated liquid/vapor of mixture is known then the pressure can be determined. This is because in the phase change region, pressure and temperature are dependent on each other. However, in the mixed region, the engineer is unable to determine the location on the P-H diagram with only temperature and pressure. Another value must also be known, like entropy, specific volume or steam quality. For example, if the engineer was asked to determine the enthalpy of water at 212 F, 14.7 PSIA, it would be impossible, because the point could be located anywhere in between the saturated vapor and liquid lines, along the constant pressure/temperature lines in the dome.

Entropy lines on the P-H diagram are shown as downward sloping curves, refer to the figure below.

Entropy increases as enthalpy is increased in all three regions. Entropy is shown to decrease in the super heated steam region when pressure is increased. Constant entropy lines are used during an isentropic process, which means a conversion in which entropy is held constant. One common process is the flow of steam through an ideal steam turbine. Steam enters the turbine at a high pressure and leaves at a lower pressure, transmitting the thermal energy to mechanical work.

The final set of lines on the P-H diagram is the constant specific volume lines, shown below. Specific volume lines are nearly horizontal in the vapor region and nearly vertical in the liquid region. It can be seen that in the liquid region, there is very little change in specific volume. However, in the superheated vapor region, there is a wide range of specific volume. Specific volume is shown to increase as pressure is lowered.

Although the P-H diagram is a very powerful tool, typically steam tables are used to solve steam problems. Steam tables are simply a listing of the values of specific volume, enthalpy and entropy as a function of pressure and temperature at the saturated liquid and vapor curves.