Specific enthalpy increments for propan-1-ol at temperatures up to 573.2 K and 11.3 MPa

doi:10.1006/jcht.1999.0594Available online at http://www.idealibrary.com on

J. Chem. Thermodynamics 2000, 32, 329339

Specific enthalpy increments for propan-1-ol attemperatures up to 573.2 K and 11.3 MPa

C. J. Wormalda and M. D. VineSchool of Chemistry, University of Bristol, Bristol, BS8 1TS U.K.

Measurements of specific enthalpy increments for propan-1-ol are reported. A counter-current water-cooled flow calorimeter was used to measure 85 enthalpy increments over thetemperature range (423.2 to 573.2) K at pressures from (0.1 up to 11.3) MPa. Extrapolationof the gas phase measurements to zero pressure gave values in excellent agreement withpure component ideal gas enthalpies calculated from spectroscopic data. Values of thespecific enthalpy of vaporisation derived from the measurements are in agreement withother work and are well fitted by a modification of the Watson equation. A method for thecalculation of the two phase enthalpypressure envelope is described. c 2000 Academic Press

KEYWORDS: enthalpy increments; propanol; flow calorimeter

1. IntroductionA counter-current water-cooled heat-exchange flow calorimeter for the measurement ofenthalpy increments at temperatures up to 700 K and pressures up to 15 MPa has beendescribed.(1) The calorimeter operates by pumping liquid or a liquid mixture from areservoir at atmospheric pressure through a flash vaporiser at a controlled temperature andpressure and allowing the hot vapour to condense in a water-cooled heat exchanger. Thecooling water was supplied at a temperature of about 275 K and the flow rate was adjustedso that the condensate leaving the calorimeter was at a temperature close to 298.15 K,the reference state temperature. Enthalpy increments were calculated from the flow rateof the cooling water, the flow rate of the fluid, and the temperatures of the incomingand outflowing water and fluid. The calorimeter was tested by making 90 measurementsof enthalpy increments for steam over the range of temperatures (423.2 to 623.2) K atpressures up to 10.3 MPa. These agreed with steam tables to within 0.5 per cent. Thecalorimeter has been used to measure enthalpy increments for methanol,(2) ethanol,(3)propanone,(4) n-hexane,(1) benzene,(5) (propanone + n-hexane),(6, 7) and (propanone +benzene).(8) Enthalpy increments for propan-1-ol are now reported.

aTo whom correspondence should be addressed.

00219614/00/030329 + 11 $35.00/0 c 2000 Academic Press

330 C. J. Wormald and M. D. Vine

0.0

0.4

0.6

0.8

1.0

h/

(103

kJk

g1 )

1.2

1.4

4.0

423.2 K

453.2 K

498.2 K

528.2 K

538.2 K

558.2 K573.2 K

548.2 K

p /MPa

8.0 12.0

FIGURE 1. Specific enthalpy increments 1h for propan-l-ol plotted as a function of the pressure p., table 1.

2. ExperimentalEnthalpy increments were measured with the counter-current heat-exchange calorimetricapparatus described previously.(1) The mole fraction purity of the propan-1-ol was 0.996,and it was used as supplied. The alcohol was pumped at a rate of approximately 0.15 g s1through the apparatus. It was usually possible to adjust the flow rate of the cooling waterso that the temperature of the alcohol leaving the calorimeter differed by little more than (2or 3) K from the standard state temperature 298.15 K. At the temperatures T = (558.2 and573.2) K, the fluid leaving the apparatus was analysed by gasliquid chromatography tocheck for possible decomposition, but no evidence of this was found. Enthalpy incrementsmeasured over the temperature range T = (423.2 to 573.2) K at pressures from p = (0.1to 11.3) MPa, and calculated as described below, are listed in table 1 and plotted againstpressure in figure 1. Temperatures are on the IPTS 1968 scale.

3. Calculation of enthalpy incrementsAt the pressure p of the experiment, a stream of propan-1-ol vapour at a high temperatureT1 enters the water-cooled heat-exchange calorimeter and emerges as a liquid at atemperature T2 which is close to 298.15 K, and at the same pressure. Energy lost by themixture is gained by the cooling water. Measurement of the water flow rate and temperature

Specific enthalpy increments for propan-1-ol 331

TABLE 1. Specific enthalpy increments 1h/(kJ kg1) for propan-1-ol measuredrelative to the saturation pressure ps of the liquid at the standard temperature 298.15 K

TK

pMPa

1hkJ kg1

pMPa

1hkJ kg1

pMPa

1hkJ kg1

pMPa

1hkJ kg1

pMPa

1hkJ kg1

423.2 0.10 995 0.32 990 0.98 395 7.79 3940.21 992 0.43 980 3.91 394 11.1 395

453.2 0.10 1053 0.94 1014 1.38 507 7.12 5080.48 1036 0.96 1012 5.25 508 11.5 506

498.2 0.10 1145 1.85 1092 3.28 695 8.59 6910.93 1122 2.53 1057 6.58 692 11.2 684

528.2 0.1 1210 1.85 1171 3.45 1115 5.17 831 7.87 8160.18 1191 2.84 1136 4.13 1067 5.78 830 11.3 799

538.2 0.1 1239 2.07 1210 4.26 1122 5.32 1034 6.01 8970.53 1232 2.86 1174 4.31 1121 5.44 995 6.71 8780.77 1230 3.2 1155 4.99 1072 5.56 943 7.79 8601.39 1221 3.51 1150 5.18 1060 5.61 919 9.54 8531.94 1215 3.91 1133 5.24 1051 5.75 905 11.3 848

548.2 1.25 1232 5.36 1107 6.19 1023 6.65 969 7.98 9163.11 1190 5.84 1069 6.31 1004 7.20 946 9.27 8954.13 1155 6.08 1038 6.53 980 7.39 931 9.33 895

558.2 0.10 1277 1.77 1244 4.95 1165 7.30 1036 9.06 9610.84 1263 3.06 1218 6.37 1093 8.17 974 11.2 936

573.2 0.10 1309 1.63 1279 5.08 1207 8.01 1078 10.9 10030.50 1303 2.71 1260 6.51 1170 9.21 1034

rise allows the calculation of the quantity 1h where:

1h = h(p, T1) h(p, T2), (1)and this quantity is the interval ab marked on figure 2. This figure shows two enthalpypressure isotherms, one at a high temperature T1 (which is actually 498.2 K) and another at298.15 K. For clarity, two features of the 298.15 K isotherm have been exaggerated. First,the saturation pressure ps of propanol at T = 298.15 K is 0.0027 MPa but has been plottedas 0.27 MPa. Second, the slope (dh/dp) of the line db, which can be calculated from theformula v(1 T ) where v is the specific volume and is the isobaric expansivity, has aslope of 0.86 J MPa1, but has been plotted with a slope of 8.6 J MPa1.

The desired quantity is the difference 1h between the molar enthalpy of the alcoholat (p, T1) and the standard state conditions T = 298.15 K and p = ps where ps is the


ps 2

Liquid at 298.15 K

Liquid at T1/K

hvap(T)

hvap(298.15 K)

Gas at T1/K

a

g

fe

db

h

0

200

400

600

h/(kJ

kg

1 ) hid(298.15 K)

1000

hid(T1)

4

p /MPa

6 c 8 10

FIGURE 2. The relationship between a measured enthalpy increment 1h at temperature T1, theisotherm at 298.15 K, and the ideal gas enthalpy at temperature T1. For clarity the isotherm at298.15 K has been modified by multiplying the saturation pressure ps by 100, and by multiplyingthe slope of the line db by 10.

saturation pressure at T = 298.15 K:

1h = h(p, T1) h(ps, 298.15 K). (2)

1h is the increment ac in figure 2 and can be calculated from 1h by the addition of twoterms;

1h = 1h + T2

298 Kcp(p, T )dT +

ppsv(1 T )dp, (3)

where cp,m is the specific heat capacity of the alcohol, v is the specific volume, and isthe isobaric expansivity at T = 298.15 K calculated from density measurements listed inreference 9. The cooling water flow rate was adjusted until T2 was close to 298.15 Kso that the cp integral was small and the pressure and temperature dependence of cpcould be neglected. Figure 2 corresponds to a case in which T2 = 298.15 K. Smallcorrections for heat leaks and for the rate at which kinetic energy enters the calorimeterwhen the pressure is low were made as previously described.(1) Systematic errors on themeasurements are estimated to be no greater than 0.3 kJ kg1. Random errors arosemainly from fluctuations in the operation of the metering pump supplying the alcohol andwere estimated to be 2 kJ kg1. In the critical region, small fluctuations in the flowrate of the alcohol, and in the pressure and temperature, produced large fluctuations in themeasured enthalpy increments. The random error in this region was therefore larger, butwas estimated to be no more than 8 kJ kg1.


4. The gaseous region at low pressuresAn important test of the accuracy of the measurements is to extrapolate them to zeropressure and to make a comparison with ideal gas enthalpies obtained from spectroscopicmeasurements or gas phase heat capacities. Figure 3a shows gas phase enthalpies atpressures below 6 MPa extrapolated to zero pressure. The zero pressure intercepts areshown in figure 3b where they are compared with ideal gas enthalpies calculated fromspectroscopic measurements obtained by Chao and Hall.(10) These enthalpies are reportedon a scale for which the ideal gas enthalpy is zero at T = 0 K, whereas our measurementsare on a scale for which the enthalpy of the liquid at T = 298.15 K and p = ps is taken aszero. The relationship between the two scales is best explained with reference to figure 2.Point d on the figure is the reference state at T = 298.15 K and ps for which the enthalpyof the liquid is taken as zero. Point g, which is the ideal gas enthalpy at temperature T1, isreached by summing three contributions. The first is the specific enthalpy of vaporisation1hvap of the liquid at T = 298.15 K, which is the enthalpy increment de. The second isthe incremental change of enthalpy ef of the vapour at T = 298.15 K as it expands fromthe saturation pressure ps to p = 0. The third is incremental change fg of the ideal gas asthe temperature is increased from T = 298.15 K to T1. The ideal gas enthalpy hig(T1) isgiven by:

hig(T1) = hl(298.15 K, ps)+1hvap(298.15 K)+ 0

ps(h/p)T dp+

T298.15 K

(h/T )dT .

(4)The enthalpy hl of the liquid at T = 298.15 K and p = ps is zero by definition.Wilhoit and Zwolinsky(9) list several values of the enthalpy of vaporisation 1hvap atT = 298.15 K. As the value (795 12) kJ kg1 was obtained by two groups of workers,Williamson and Harrison(11) and Matthews and McKetta,(12) and it is in the middle ofthe range of available values, we judged it to be the best. For gaseous propan-1-ol thequantity (h/p)T = B T (dB/dT ) is the isothermal JouleThomson coefficient oof the vapour, so the first integral is easily evaluated and to a good approximation it isequal to o(0 ps). The value of o for propan-1-ol at T = 298.15 K was estimatedfrom second virial coefficient measurements, and is approximately 10 dm3 mol1.The saturation pressure of propan-1-ol is 0.0027 MPa at T = 298.15 K, and the quantityo ps = (0.4 0.1) kJ kg1, which is negligible. To evaluate the second integral, thequantity (h/T ) can be calculated from the ideal gas enthalpies of Chao and Hall,(10)but it is simpler just to fit these enthalpies to a polynomial in powers of the temperature.Equation (4) reduces to the sum of the specific enthalpy of vaporisation (79512) kJ kg1and the perfect gas enthalpy increments calculated by Chao and Hall(10) on a scale forwhich the increment at T = 298.15 K is taken as zero. Values of hig(T1) are given by theequation:

{hig(T1)hig(298.15 K)}/kJ kg1 = 481.7+0.6014(T/K)+1.498 103(T/K)2. (5)The curve shown in figure 3(b) was calculated from equation (5). Agreement betweenthe calculated enthalpy increments and those obtained by extrapolation of the table 1measurements to zero pressure is to within 1 per cent.


0

1.0

1.1

1.2

h/

(103

kJ

kg1 ) 1.3

1.4

1

573.2 K

a b

2

558.2 K

p /MPa T /K

3

548.2 K528.2 K

498.2 K453.2 K

423.2 K

4 5 400 500 600

FIGURE 3. a, Specific enthalpy increments1h for propan-l-ol at low pressures plotted as a functionof pressure p, showing the extrapolation to zero pressure; , table 1. b, Zero pressure values of thespecific enthalpy of propan-l-ol, obtained from figure 1, shown plotted against temperature. The curvewas fitted to ideal gas enthalpies derived from spectroscopic measurements by Chao and Hall.(10)

5. Enthalpies of vaporisationThe four isotherms at temperatures between (423.2 and 528.2) K start at low pressuresin the gas phase region, they intersect the upper part of the two phase boundary at thedew point pressure, cross the two phase region, intersect the lower part of the boundaryat the bubble point pressure, and continue to higher pressures in the liquid phase. Thevertical lines which cross the two phase region are at the saturation pressure of the alcohol.Saturation pressures were calculated from the equation:

ln(p/po) = 183.61+ 0.02387(T/K) 11953(K/T ) 27.082 ln(T/K), (6)which fits the vapour pressure of propan-1-ol from standard atmospheric pressure po =0.101325 MPa up to the critical pressure (5.175 MPa) to within 0.05 MPa, which isadequate for our purposes. The difference between the specific enthalpies of the saturatedvapour1h(g) and the saturated liquid1h(l) is the specific enthalpy of vaporisation1hvap,and all three quantities are listed in table 2.

Enthalpies of vaporisation for propan-1-ol over the temperature range T = (414.2 to470) K have been measured by Radosz and Lydersen(13) who fitted their measurements toan equation with four disposable parameters a1 to a4. The first term was a1(1 Tr)1/3 andhigher terms of similar form had exponents 2/3, 5/3, and 6/3. Their measurements cannotbe fitted with adequate accuracy by the Watson(14) equation. Vine and Wormald(3) foundthat the Watson equation was a poor fit to the enthalpies of vaporisation of ethanol, andthey suggested the equation

1vaph(T ) = 1vaph(Tb){ax + (1 a)xm}n, (7)where

x = (1 T/Tc)(1 Tb/Tc)1, (8)


TABLE 2. The specific enthalpies h(liq) and h(gas) at the satura-tion temperature T and pressure p, the specific enthalpy of vapor-isation 1h(vap) and the uncertainty 1h(vap) on this quantity, forpropan-l-ol. The values at T = 298.15 K and the normal boilingtemperature 370.9 K were obtained from the literature, all other

values were obtained from the table 1 measurements

TK

psMPa

h(liq)kJ kg1

h(gas)kJ kg1

1h(vap)kJ kg1

1h(vap)kJ kg1

298.15 0.0026 795 12370.9 0.1013 685 10

423.2 0.546 390 975 585 10453.2 1.13 515 1005 490 12498.2 2.75 700 1050 350 12528.2 4.51 860 1050 190 15

and a, n, and m are disposable parameters. When a = 1 the equation reduces to that ofWatson.(14) The equation was tested by fitting 30 values of the enthalpy of vaporizationof water from Tb to Tc obtained from steam tables. The best fit parameters for water area = 1.1286, m = 2.9508, and n = 0.3967. These fit the data with a standard deviationof 4 kJ kg1 whereas the standard deviation obtained with the Watson equation was26 kJ kg1.

To obtain an equation which best fits the specific enthalpy of vaporisation of propan-1-ol, we inspected the database of thermodynamic measurements on alcohols compiled byWilhoit and Zwolinsky.(9) At the normal boiling temperature 370.69 K, we chose the value1hvap(Tb) = (690 10) kJ kg1 which is the mean of the value 694 kJ kg1 obtainedby Williamson and Harrison(11) and 685 kJ kg1 obtained by Mathews and McKetta.(12)The specific enthalpies of vaporisation obtained by Radosz and Lydersen(13) and our ownvalues listed in table 2 were included in the data set fitted. The parameter m in equation (7)was set at m = 3. The best fit parameters are 1hvap(Tb) = 679 kJ kg1, a = 1.011,and n = 0.453, and the standard deviation of the fit was 10 kJ kg1. The 1hvap(T )curve for propan-1-ol is shown plotted against reduced temperature in figure 4. It is soclose to the curve fitted by Radosz and Lydersen(13) to their own data that it is difficultto distinguish one from the other. Figure 4 shows the enthalpies of vaporisation obtainedfrom our measurements to be in good agreement with other work.

6. Constructing the two phase boundaryTo construct the two phase boundary on the enthalpy pressure diagram shown in figure 1,it is convenient first of all to fit the specific enthalpies of vaporisation to an equation inwhich the argument is a function of reduced pressure pr rather than reduced temperatureTr. Equation (7) is again of suitable form, and it was soon established that the parameter


0.00

200

400

h v

ap/(k

Jkg

1 ) 600

800

0.2 0.4

T /Tc

0.6 0.8 1.0

FIGURE 4. Specific enthalpies of vaporisation of propan-l-ol plotted as a function of the reducedtemperature T/Tc. , Table 2, derived from the table 1 measurements. 4, Radsoz and Lydersen(13), Williams and Harrison(11) and Matthews and McKetta.(12)

m = 1.5 was a good choice;1hvap(p) = 1hvap(po)(ay + (1 a)y1.5)n, (9)

where y is given byy = {ln(p/Pc)}/{ln(po/Pc)}. (10)

The specific enthalpy of vaporisation 1hvap(po) at the standard pressure po =0.101325 MPa is of course the same quantity as 1hvap(Tb). As before, 1hvap(po)was treated as an adjustable parameter. Least squares optimisation gave 1hvap(po) =685 kJ kg1, a = 1.7035, and n = 0.456. With these parameters, equation (9) fits thevaporisation enthalpies listed in table 2 with a standard deviation of = 8 kJ kg1,which is slightly better than the fit obtained using equation (7). Again the curve is almostindistinguishable from that shown in figure 4.

To construct the two phase envelope, we first simplified figure 1 by subtracting idealgas enthalpies calculated from equation (5) from the measurements listed in table 1 and soobtained residual enthalpy increments

1hres = 1h(p)1hig. (11)Residual enthalpy increments were then plotted against reduced pressure pr as shown infigure 5. The use of reduced pressure facilitates comparison with similar diagrams forother fluids. The two phase envelope is now more symmetric than before. The mid-pointof each of the four vertical sections, which are the enthalpies of vaporisation, was marked,and a curve through these mid-points was drawn and extrapolated to p/Pc = 1. In thisway a value of the residual enthalpy hc at the critical point was obtained, and found to


0.0

0.6

0.4

h r

es/ (

103

kJk

g1 ) 0.2

0.0

0.4

528.2 K

498.2 K

453.2 K

423.2 K

0.8

p /Pc

1.2 1.6

FIGURE 5. Residual specific enthalpy increments for propan-l-ol plotted against reduced pressurep/Pc. The length of the vertical lines is a measure of the specific enthalpy of vaporisation. The brokencurve is the locus of the mid-points of the vertical lines, and was calculated from equation (13)as described in the text. The curve intersects the two-phase boundary at the critical point residualenthalpy hc = 255 kJ kg1. , Calculated from table 1 measurements.be hc = (255 10) kJ kg1. At the pressure po = 0.101325 MPa, which is a reducedpressure of pr = 0.019, the enthalpy of vaporisation calculated from equation (9) with theparameters given above is (685 5) kJ kg1. At this pressure, the residual enthalpy ofthe liquid at the bubble point pressure is the sum of two terms, the residual enthalpy of thegas and the specific enthalpy of vaporisation of the liquid:

1hres = po

0(h/p)T dp +1hvap. (12)

Here (h/p)T can be calculated from the isothermal JouleThomson coefficient o =B T (dB/dT ) of the vapour at the normal boiling temperature 370.69 K divided bythe molar mass. The integration is carried out from p = 0 to p = po. Second virialcoefficients for propan-1-ol are listed in Dymond and Smiths compilation.(16) These wereplotted against temperature, and from the gradient at T = 370.69 K the value of wasestimated to be (4.00 0.5) dm3 mol1, and the value of the integral in equation (12)was found to be (71) kJ kg1. The specific enthalpy of vaporisation at T = 370.69 K is(685 5) kJ kg1. The mid-point at 342.5 kJ kg1 of a vertical line drawn on the figurecorresponding to an enthalpy of vaporisation of 685 kJ kg1 fixes the low pressure limitof the mid-point curve. As required by equation (12), this mid-point is plotted in figure 5at (342.5+ 7) kJ kg1 and at po/Pc = 0.019, which is almost zero reduced pressure.

An equation which can adequately describe the locus of the mid-points was sought,but the few data points available from this work alone made it difficult to discern the


shape of the curve. Accordingly we constructed diagrams similar to figure 5 for water,(15)methanol,(2) and ethanol,(3) and again drew mid-point curves. It was found that the locusof the mid-points of the two-phase region residual enthalpies for each of these fluids canbe fitted to within experimental error by an equation of the form

hmid = {0.51hvap(po) hc}(1 pr)z, (13)where

z = 1+ s{ln(p1r )}. (14)When the adjustable parameter s = 0, the equation generates a linear mid-point linesimilar to the rectilinear diameter law for coexisting liquid and gas densities. The mid-points of the two-phase region liquid and gas residual enthalpies for propan-1-ol can befitted by a linear function only down to pr = 0.4; to fit the mid-points at lower reducedpressures requires a function which is not far from linear at pr > 0.4 and which changesmore quickly as pr approaches zero. The logarithmic functionality given by equation (14)fulfills this requirement. The best value of the parameter s was found to be s = 0.5. Finallyat each value of pr the mid-point residual enthalpy was calculated from equations (13)and (14), the dew point enthalpy h(gas) was obtained by subtracting one half of theenthalpy of vaporisation calculated from equation (9), and the bubble point enthalpy h(liq)was calculated by adding the same amount.

To calculate the two-phase envelope shown in figure 1, it is only necessary to add perfectgas enthalpies calculated from equation (5). As the ordinate in figure 1 is pressure ratherthan temperature, it is convenient to generate an equation which expresses the saturationtemperature Tsat as a function of the pressure. The saturation temperature of propan-1-ol,obtained by fitting vapour pressure measurements as a function of ln(p/po), is given bythe equation

Tsat/K = 370.9+ 26.638{ln(p/po)} + 1.9917{ln(p/po)}2.5. (15)The alternative procedure is to solve equation (6) iteratively to yield values of Tsat at eachchosen pressure, but it is less convenient. Ideal gas enthalpies can now be calculated attemperature Tsat, and the transformation of the two phase envelope shown in figure 5 backto that shown in figure 1 is straightforward. Values of the mid-point curve hmid(1) shownin figure 1 were calculated from values of hmid(5) shown in figure 5 from the equation

hmid(1) = hig hc hmid(5), (16)where hig was calculated from equation (5), and hmid(5) was calculated from equation (13).Addition or subtraction of one half of the enthalpy of vaporisation calculated fromequation (9) generates the two phase envelope shown in figure 1.

REFERENCES

1. Wormald, C. J.; Yerlett, T. K. J. Chem. Thermodynamics 1985, 17, 11711186.2. Yerlett, T. K.; Wormald, C. J. J. Chem. Thermodynamics 1986, 18, 719726.3. Vine, M. D.; Wormald, C. J. J. Chem. Thermodynamics 1989, 21, 11511157.4. Yerlett, T. K.; Wormald, C. J. J. Chem. Thermodynamics 1986, 18, 317379.5. Vine, M. D.; Wormald, C. J. J. Chem. Thermodynamics 1991, 23, 11751180.


6. Wormald, C. J.; Yerlett, T. K. J. Chem. Thermodynamics 1987, 19, 215224.7. Al-Bizreh, N.; Wormald, C. J.; Yerlett, T. K. J. Chem. Soc. Faraday Trans. 1 1988, 84, 3587

3596.8. Wormald, C. J.; Yerlett, T. K. J. Chem. Thermodynamics 1992, 24, 493498.9. Wilhoit, R. C.; Zwolinsky, B. J. J. Phys. Chem. Ref. Data 1973, 2, 72.

10. Chao, J.; Hall, K. R. Int. J. Thermophysics 1986, 7, 431442.11. Williamson, K. D.; Harrison, R. H. J. Chem. Phys. 1957, 26, 14091411.12. Mathews, J. F.; McKetta, J. J. J. Phys. Chem. 1961, 65, 758762.13. Radosz, M.; Lydersen, A. Chem. Ing. Tech. 1980, 52, 756757.14. Watson, K. M. Ind. Eng. Chem. 1943, 35, 398408.15. Haar, L.; Gallagher, J. S.; Kell, G. S. NBS/NRC Steam Tables. Hemisphere: 1984.16. Dymond, J. H.; Smith, E. B. The Virial Coefficients of Pure Gases and their Mixtures. Clarendon

Press: Oxford. 1980.

(Received 29 June 1999; in final form 23 August 1999)WE-175

IntroductionExperimentalTable 1Fig. 1

Calculation of enthalpy incrementsFig. 2

The gaseous region at low pressuresFig. 3

Enthalpies of vaporisationTable 2Fig. 4

Constructing the two phase boundaryFig. 5

References

Documents

Specific enthalpy increments for propan-1-ol at temperatures up to 573.2 K and 11.3 MPa