Construction of a Mollier Diagram
Properties of humid air are usually described by means of the Mollier diagram. The Mollier diagram is constructed for a certain air pressure, normally for the value
P — 1.013 bar = 760 mm Hg = 1 atm,
Which is the so-called standard atmosphere pressure. As suggested in Examples 1 and 2, a Mollier diagram can be used only when the total pressure is the same or almost the same as the pressure for which the diagram wTas constructed.
The abscissa of the Mollier diagram is humidity %. The axis is provided writh a pitched scale. A straight line is drawn with a 45° angle to the abscissa, and it is provided with an enthalpy scale (hk) according to the equation hk = lho ■ x = 2501.6 • x, kj/kg (Fig. 4.8). Consequently the enthalpic scale (hj,) is also pitched.
Now we construct this oblique-angled coordinate system with isotherms.
6 = 0 °C, hk = cp, e + x(cphe+ lho) = xlho = 2501.Y, kj/kg.
While the bk scale was constructed with the equation bk = 2501 x, it is noticed that the isotherm 0 = 0 °C joins the abscissa.
For 0 = 0ig — bk = CpjOi +x(CphOi + lho) = 1.0060] +*(1.850! +2501) .
The isotherm 6 = is a straight line in the bk —x coordinate system. The isotherms are not exactly parallel due to the term When
0j < 0 °C, the isotherms go downward (relative to the abscissa), and when > 0 °C, the isotherms go upward.
The isotherms cut the y-axis at % = 0 or = Cpfi. When cpi is held constant, it follows that the temperature scale is pitched.
When the saturation curve (<p = 100%) and other curves of relative humidity (<p) are added, the Mollier diagram is complete (Fig. 4.9).
Construct a Mollier diagram for air, when the total pressure of air is 875 mbar.
First we construct the hk — x coordinate system according to the instructions given above.
We provide the y-axis x = 0 with temperatures with the help of the equation hk = cpi6 + x(cph0+ lho) = cpi0 = 1.0060, kj/kg.
When 9 = -5 °C, hk = -5.03 kj/kg, and when 0 = +5 °C, hk= + 5.03 kj/kg, etc. Points where the isotherms cut the y-axis are located pitched.
Next we draw the saturation curve in the hk-x coordinate system. Vapor pressures can be calculated with Eqs. (4.106) and (4.108) or taken directly from the tables. The humidity x’ corresponding to the saturation pressure pf,(t) is calculated with Eq. (4.83) noting that p = 0.875 bar. The enthalpy of humid saturated air is calculated with Eq. (4.94):
H’k = 1.006fl + x'(l.850 + 2501), kj/kg.
The saturation curve is drawn through points (x’, h’k ), calculated for different temperatures. At the same time the other ends of isotherms are determined, and because they are straight lines, they can now be drawn.
The curves of relative humidity <pu <p2, ■ ■ . can now be easily drawn writh the help of the isotherms by just calculating the humidity corresponding to <P], <Pi, . . . and using the already constructed isotherms.
With high temperatures the x’ values will not fit into the diagram. Then the hk values have to be calculated with smaller x values in order to draw the isotherms. In Table 4.6 these values are calculated with values x = xs0% at various temperatures. Drawing the fundamental axes and isotherms with the instructions given above and the saturation curve with the help of Table 4.6 leads to the Mollier diagram in Fig 4.10<j.
TABLE 4.6 Values Calculated for the Construction of the Mollier Diagram When the Total Pressure is p 0.875 bar
In Figs. 4.10b-d some commonly used Mollier diagrams are presented. The diagram in Fig. 4.106 is valid for the air pressure p — 1 bar and is used in conventional calculations of air conditioning technology. Figure 4.10 c is an American version of Fig. 4.106. It is a mirror image, and the direction of the scales is reversed. A diagram that covers a very wide temperature range and is therefore excellently suited to applications in the field of process technology is presented in Fig. 4.10o!. This diagram is used, for example, in the technical design of the drying part of a paper machine. In Fig. 4.1 Off the enthalpy scale is on the abscissa and the curves of constant enthalpy are straight lines. The curves give the humidity relation, which is defined as f= x/x'(6), where x'(6) is the humidity of saturated air at temperature 6. Humidity relation ^and relative humidity ip are different figures and should not be mixed.
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