Point of Interest (POI) for Ammonia/ R717

Definition

Where it occurs

Special features

How to draw it

(1) Locate the mouse at a point on the graph and left-click. The table will then report the corresponding thermodynamic properties. These are reported in the 'current' row: pressure, temperature, specific volume, enthalpy, entropy, dryness. The 'change' row reports the difference in properties between the current POI and the previous POI.

When you attempt to plot in the subcooled region, the POI is moved horizontally onto the saturated liquid line. This is because pressure increases exponentially with entropy in this region.

(2) Choose a pair of inputs from the drop down box. Options are: temperature-entropy; pressure-enthalpy; temperature-pressure; temperature-dryness fraction; pressure-dryness fraction. Complete the text boxes and press the "SetPOI" button.

Hint, if you want precise properties of saturated liquid set the dryness fraction to zero. For saturated vapour set the dryness fraction to one.

Restrictions, limitations and innaccuracy

The theory

I extracted properties from three sources. The datum was in line with Rogers and Mayhew: saturated liquid at 233K.

Saturation pressures are available from NIST ; they provide coefficients for an Antoine equation. $$ log_{10} ( p_{sat}) = c_0 + \frac{ c_1 }{ T + c_2} $$ The inverse function is found analytically.

Scaled specific volumes are published in Ziegler and Trepp $$ v'_l = A_1+A_2p_r+A_3T_r+A_4T_r^2 \qquad \qquad liquid $$ $$ v'_v = T_r/p_r + C_1 + C_2 T_r^{-3} + C_3 T_r^{-11} + C_4 p_r ^2 T_r^{-11} \qquad \qquad vapour $$ where \(T_r=T/T_B\) and \(p_r=p/p_B\) are reduced values using \(T_B =100K\), \(p_B=10 bar \).

Ziegler and Trepp also publish liquid enthalpies and liquid entropies . I adjusted their datum. $$ h_l(kJ/kg) = 420.2 + R T_B (B_1(T_r-T_{ro})+B_2(T_r^2-T_{ro}^2)/2 + B_3(T_r^3-T_{ro}^3)/3) + R T_B ( A_1(p_r-p_{ro})+A_2(p_r^2-p_{ro}^2)/2-A_4(p_r-p_{ro})/(T_r^2)) \qquad \qquad liquid $$ where R is the specific gas constant for ammonia and reduced reference values are \(p_{ro}=2 , T_{ro}=3.2252\).

Ziegler and Trepp also publish data for vapour enthalpy and vapour entropy, but I was unable to make these work accurately in the data range. Instead I fitted data in a set of steam tables to quadratic equations, for saturation temperatures of 223K, 273K and 323K. For an isobaric change in enthalpy at the corresponding pressures \(p_1, p_2\) or \(p_3\), $$ h_{v}(p_i,T)= C_{0,i}+C_{1,i}T+C_{i,2}T^2 \; at \;p_i \qquad \qquad p_1=0.4089 bar; \; p_2 = 4.295 bar; \; or \; p_3 = 20.33 bar $$ The three quadratic coeffients C are different for each of the three pressures. For the purposes of an arbitrary pressure p, Rogers and Mayhew write a section on the 'graphical determination of entropy and enthalpy'. For an isothermal change in enthalpy , $$ h_v(p,T) = h_v(p_i,T) + \int_{p_i}^p \frac {d(v/T)}{d(1/T)} dp \qquad choose \; p>p_i$$ Vapour entropy is treated similarly. $$ s_v(p_i,T) = s_{g,i} + C_{1,i}ln(T/T_{sat,i} ) + 2C_{2,i}(T-T_{sat,i}) \; at \;p_i \qquad \qquad p_1=0.4089 bar; \; p_2 = 4.295 bar; \; or \; p_3 = 20.33 bar $$ where \(s_{g,i}\) is entropy of saturated vapour at pressure \(p_i\). From the same section in Rogers and Mayhew $$ s_v(p,T) = s_v(p_i,T) + R \int_{p_i}^p (\frac{dV}{dT})_p dp \qquad choose \; p>p_i $$

Exercises

Links

My notes on refrigeration

Checks

Predictions from algorithms were checked against the property tables ( see here Rogers and Mayhew ).