CONSTRUCTION OF A LOW TEMPERATURE SIMPLIFIED
CONSTRUCTION OF A LOW TEMPERATURE SIMPLIFIEDPSYCHROMETRIC CHARTTechnical ReportSubmitted in partial fulfilment of the requirements for the course ofDesign of Air Conditioning Systems (TH819)inMechanical EngineeringBySthavishtha B.R.(13ME125)Under the supervision ofProf. T.P. Ashok Babu(Dean Faculty Welfare)DEPARTMENT OF MECHANICAL ENGINEERINGNATIONAL INSTITUTE OF TECHNOLOGY KARNATAKASURATHKAL, MANGALORE - 575025 (INDIA)April, 2017
ACKNOWLEDGEMENTI am deeply indebted to Prof. T.P. Ashok Babu for guiding me throughout the course of thiswork. Without his support and motivation, this work would not have been successful enoughto be completed within the stipulated time.Finally, I am thankful to the Almighty for showering his blessings, thus enabling me tocomplete this course and its project work satisfactorily.
NOMENCLATURE๐๐Partial pressure (๐ 2 )๐ ๐ปRelative Humidity๐คSpecific Humidity (๐๐ /๐๐ ) Enthalpy (๐๐ฝ /๐๐ )tDry bulb temperature ( C)ฮฃSigma heat function๐ Gas constant (๐๐ฝ /๐๐๐พ)TTemperature (K)SubscriptsaDry airatmAtmosphericvVapoursSaturatedfSaturated water (specifically for enthalpy)Superscript*Saturated conditions (during adiabatic saturation)
ABSTRACTThe current study attempts to construct a low temperature psychrometric chart whose drybulb temperature varies from -60 C to 0 C at constant atmospheric pressure. For thispurpose, a numerical code was developed in MATLAB and the required thermodynamic datawas imported from a file. The constructed chart has also been validated with an available lowtemperature psychrometric chart (in the reference section), which satisfies the credibility ofthe developed code and the method. In the future, this code can be extended to constructcharts operating in other vapour systems or at other altitudes with sufficient accuracy. Thisreport also contains the methodology required to construct the psychrometric chart along withthe MATLAB numerical code for reference.
TABLE OF CONTENTS123INTRODUCTION . 71.1Overview of Psychrometrics and Psychrometric Chart . 71.2Motivation . 71.3Literature Review . 71.4Psychrometric Relations . 7METHODOLOGY . 92.1Saturation Line . 92.2Constant Relative Humidity Lines . 102.3Constant Specific Volume Lines . 112.4Constant Thermodynamic Wet Bulb Temperature Lines . 112.5Constant Enthalpy lines . 122.6Sensible Heat Factor (SHF) Protractor. 13RESULTS AND DISCUSSIONS . 143.1Psychrometry chart from the current study . 143.2Validation of the Chart obtained from the present study . 143.3 Comparison of Saturation water Vapour Pressure with data from ASHRAE [9] andcorrelation [9, 12] . 164NUMERICAL CODE. 185CONCLUSIONS . 266APPENDIX . 276.1Thermodynamic Data from ASHRAE [9] . 276.2 Percentage Deviations of the psychrometric values obtained along constant enthalpylines on comparison with reference chart [11] and ASHRAE table [9] . 286.3 Percentage Deviation of saturated water vapour pressure between the ones fromASHRAE [9] and correlation [9,12] . 297REFERENCES . 31
LIST OF FIGURESFigure 2.1. Plot of saturation line in the psychrometric chart . 10Figure 2.2. Plot of constant relative humidity lines in the psychrometric chart . 10Figure 2.3. Plot of constant specific volume lines in the psychrometric chart . 11Figure 2.4. Plot of constant wet bulb temperature lines in the psychrometric chart . 12Figure 2.5. Constant enthalpy lines in the psychrometric chart . 13Figure 3.2. Validation of the constant specific volume line from the current study withreference chart [11] . 14Figure 3.1. Low temperature simplified psychrometric chart obtained from the present study. 15Figure 3.3. Validation of the constant enthalpy line from the current study with the referencechart [11] . 16
1INTRODUCTION1.1 Overview of Psychrometrics and Psychrometric ChartPsychrometrics is a subject which deals with the determination of thermodynamic propertiesof gas-vapour mixtures. A psychrometric chart helps in graphically representing theseproperties and enables a lay man to easily identify them without explicitly calculating themfrom the tables given in several data handbooks. The most commonly used psychrometriccharts deal with air-water vapour (or moist air) systems.Psychrometric charts have numerous applications. They can be used for analyzing thepsychrometric processes involving moist air and in determination of human thermal comfortconditions. Additionally, the properties of moist air listed in the psychrometric chart make itimperative to design air-conditioning equipments for storage of food, dryers and coolingtowers in food processing plants [1].Several standard psychrometric charts are available by ASHRAE for reference [2,9]. Theseare constructed at different altitudes (different pressures) and for a range of dry bulbtemperatures (low, high, normal and very high). In this direction, generalized psyhcrometriccharts [3] and charts at different gas-vapour systems [4,5] have also been constructed.1.2 MotivationIn polar regions and harsh climatic areas, the dry bulb temperatures may drop way below thefreezing point of water (0 C). Hence, in such cases, it becomes vital for constructing a lowtemperature psychrometric chart. Moreover, manual construction of a psychrometric charthelps the students in improving their fundamental understanding of thermodynamic relationsand psychrometric processes [6]. With this motivation, the current study aims to plot thepsychrometric chart from -60 C to 0 C dry bulb temperature at atmospheric pressure.1.3 Literature ReviewPlethora of previous works in constructing psychometric charts and tutorials have beencarried out [3,4,5,6,7]. Most of these charts have been constructed using Flash, HTML pagesor Excel spreadsheets. However, the current study attempts to construct a psychrometric chartby programming in MATLAB R2013, wherein the saturated properties of moist air areimported from excel files.1.4 Psychrometric RelationsThe psychrometric relations used in the current study are taken from [8,9]. Some of themnecessary for plotting the chart are summarized below.๐๐๐๐ก๐๐๐ ๐๐๐๐ ๐ ๐ข๐๐ ๐๐ ๐๐๐ฆ ๐๐๐ (๐ ๐๐๐๐ก๐๐ฃ๐ ๐ป๐ข๐๐๐๐๐ก๐ฆ: ๐ ๐ป ๐๐ฃ๐๐ ๐): ๐ ๐๐๐ก๐ ๐๐ฃ๐2 ๐(1)(2)
๐๐๐๐๐๐๐๐ ๐ป๐ข๐๐๐๐๐ก๐ฆ(๐๐ /๐๐ ) ๐ค 0.62198๐๐๐๐๐๐๐๐ ๐๐๐๐ข๐๐(๐3 /๐๐ ) ๐ฃ๐ ๐๐ฃ๐๐(3)๐ ๐ ๐๐๐๐๐๐๐๐๐๐๐ ๐ป๐ข๐๐๐๐๐ก๐ฆ ๐๐ก ๐ ๐๐ก๐ข๐๐๐ก๐๐๐(๐๐ /๐๐ ) ๐ค๐ 0.62198๐ธ๐๐ก ๐๐๐๐ฆ (๐๐ฝ /๐๐ ) 1.006 1.805๐ ๐ก 2501๐(4)๐๐ ๐๐(5)(6)
2METHODOLOGYThis chapter lists down the relevant method adopted to construct the low temperaturepsychrometric chart. The procedure for constructing the psychrometric chart follows [8]. Thetable containing the thermodynamic properties of moist air are taken from [9], which is alsoavailable in the Appendix. Unlike [10] which uses Virial equation of states to determine thespecific volume of moist air, this study directly imports the data present from the excel file,which is fairly simple and accurate.All psychrometric properties of moist air can be determined when any three properties areknown. Since the psychrometric chart is constructed at constant atmospheric pressure, anytwo independent variables in the psychrometric chart can help one in locating other propertiestoo. This is the basic principle adopted in the current study.2.1 Saturation LineAll the points on the saturated line correspond to a Relative Humidity of 100%. Hence, in thatcase, the saturated vapour pressure and water vapour pressure are equal. For instance, at aparticular case of dry bulb temperature equal to - 40 C,Water vapour pressure is [9]: ๐๐ ๐๐ฃ 0.01285 kN/m2At atmospheric pressure, the partial pressure of dry air is: ๐๐ ๐๐๐ก๐ ๐๐ฃ 101325 - 12.85 101312.15 N/m2Specific Humidity at saturation can be calculated from Eqn (5) as:๐ค๐ 0.62198๐๐ ๐๐ 0.6219812.85101312 .15 7.889 10-5 kg water vapour/kg dry airAs this process is repeated by computing saturated specific humidities for all possible drybulb temperatures, one can generate the saturation line.
Figure 2.1. Plot of saturation line in the psychrometric chart2.2 Constant Relative Humidity LinesRelative humidity refers to the ratio of actual vapour pressure to the saturated vapour pressure[8] according to Eqn. (2).For a certain case of 10% RH, the actual vapour pressure becomes [9]: ๐๐ฃ 0.1 ๐๐ 0.001285 kN/m2.Moreover, the specific humidity can be calculated as:๐ค 0.62198๐๐ฃ๐๐ 0.621981.285101325 1.285 7.89 10-6 kg water vapour/kg dry airThe specific humidity is computed for all dry bulb temperatures corresponding to a fixed RHto generate a constant relative humidity line. Later, this process is repeated for other relativehumidity lines, in increment of 10%.Figure 2.2. Plot of constant relative humidity lines in the psychrometric chart
2.3 Constant Specific Volume LinesFor this task, an iterative procedure [8] was adopted to compute specific volume and itscorresponding saturated dry bulb temperature. For a fixed specific volume, an approximatesaturated dry bulb temperature and its corresponding saturation pressure were estimated byinterpolation from the data in the excel file. The specific volume (approximate) was latercomputed according to Eqn. (4):๐ฃ๐ ๐ ๐ ๐287.1 (273.15 ๐ก) ๐๐101325 (1000 ๐๐ )The error between the approximate and fixed specific volume was calculated for the iterationto proceed. In the developed numerical code, the error (absolute) was fixed to be 3 10-6according to the user convenience. Moreover, the dry bulb temperature was incremented(decremented) when the approximate specific volume came out to be more than the fixedspecific volume (vice-versa). Later, the saturated specific humidity and the dry bulbtemperature lying on the fixed volume line at zero humidity was calculated. This process waslater repeated for plotting other constant specific volume lines.Figure 2.3. Plot of constant specific volume lines in the psychrometric chart2.4 Constant Thermodynamic Wet Bulb Temperature LinesThe constant wet bulb temperature corresponds to the process of adiabatic saturation,ฮฃ ๐ ๐ ๐ ๐ ฮฃ constantwhere the superscript corresponds to the saturated conditions. For instance, at a specific drybulb temperature of - 40 C, saturated specific humidity [9] is 7.889 10-5 kg watervapour/kg dry air. To calculate the saturated enthalpy, we use the Eqn. (6): 1.006 1.805๐ ๐ก 2501๐
Later, ฮฃ ๐ ๐ is calculated.Since the constant wet bulb temperature line is a line with constant slope, the temperaturecorresponding to zero specific humidity lying along this line is computed as per Eqn. (7).This was later joined to the saturated dry bulb temperature to get a straight line.๐ก ฮฃ1.006(7)Figure 2.4. Plot of constant wet bulb temperature lines in the psychrometric chart2.5 Constant Enthalpy linesRather than plotting enthalpy deviation lines on the chart, separate enthalpy lines were drawn.For a fixed enthalpy, the dry bulb temperature corresponding to zero specific humidity wasestimated by Eqn. (7).For enhancing the readability of the constant enthalpy lines, an enthalpy axis is essential. Foruser convenience, the enthalpy axis here is drawn as a straight line with a slope of 4.5 10-5,which extends as a straight line joining the corner points of the plot space : (-60, 0.25 10-3)and (-10,2.5 10-3). The equation of the line joining these corner points can be calculated tobe:๐ค 4.5 10 5 t 2.95 10 3 kg/kg.(8)Substituting the expression for w from Eqn. (8) in Eqn. (6) and simplifying, we get 9.025 10 5 t 2 1.1373๐ก 8.7535 ๐๐ฝ/๐๐(9)For a fixed enthalpy, this quadratic equation is solved to determine the dry bulb temperaturewhich lies on the enthalpy axis. Finally, a line joining this temperature to the dry bulbtemperature at zero specific humidity gives a straight line corresponding to constant enthalpy.
Figure 2.5. Constant enthalpy lines in the psychrometric chart2.6 Sensible Heat Factor (SHF) ProtractorThe protractor at the top left of the psychrometric chart is the SHF protractor. SHF is definedas the ratio of the sensible heat to total heat transfer. The presence of a protractor is necessaryto identify the direction and slope of the moist air process line. For plotting SHF lines, theprocedure available in [8] has been adopted.
3RESULTS AND DISCUSSIONS3.1 Psychrometry chart from the current studyUsing the aforementioned psychrometric equations along with the methodology (previouschapter) to plot the psychrometric curves, a numerical code had been developed in MATLABR2013 to plot the psychrometric chart from 0 to -60 C dry bulb temperature at constantatmospheric pressure of 1 atm. The relevant thermodynamic data was imported from an excelfile (also found in the Appendix). The psychrometric chart obtained from the current study isshown Fig.3.1. This chart resembles the commercial one present in [11], and is validated asdescribed later which establishes the credibility of the developed code and reliability of thepresent chart for educational purposes.3.2 Validation of the Chart obtained from the present studyThe procedure of validation is inherent for every numerical code and method. Hence, torender the credibility of the established code and its developed chart, validation of specificvolume lines (at 0.76 m3/kg) and enthalpy lines (at -20 kJ/kg) has been performed with thedata points extracted from the reference chart [11]. The data points and the lines in Figs. 3.2and 3.3 are quite close to each other, thus confirming the validity of the present study.Figure 3.1. Validation of the constant specific volume line from the current study withreference chart [11]
Figure 3.2. Low temperature simplified psychrometric chart obtained from the present study
Figure 3.3. Validation of the constant enthalpy line from the current study with the referencechart [11]For a detailed analysis of the psychrometric values obtained from the current study, they havebeen compared with the values extracted from the reference chart [11] by calculating thepercentage deviations at constant specific enthalpy lines over the entire dry bulb temperaturerange. This will allow the reader or the user to obtain the psychrometric values from thischart with an uncertainty range.The percentage deviations over the range of the chart along constant enthalpy lines can befound in Appendix 6.2 and Psychro Chart Deviations excel file, which can be found inFolder 4 - Matlab files and Program corrections 20-04-2017. As a consequence of thisvalidation study, the values were found to lie within an absolute deviation of 0.555% to2.455% in comparison to the reference chart [11], which deems the current study to beaccurate. Since the available reference chart [11] extends up to a dry bulb temperature of -50 C, all deviations of the chart from the current study have thus been studied till thistemperature. However, the specific enthalpy of dry air from this chart has been comparedwith the data in ASHRAE [6] to render credibility to the validation study over the entire lowtemperature range. Thus, the chart obtained from the current study is equally accurate asexisting commercial charts, with an uncertainty of less than 2.455 %.3.3 Comparison of Saturation water Vapour Pressure with data from ASHRAE[9] and correlation [9, 12]A numerical code was developed in MATLAB (available in Chapter 4 - Numerical Code) tocompute the saturated vapour pressure values from this correlation, which was latercompared with ASHRAE data [9] (also in Appendix).
The correlation available for calculating the saturation water vapour pressure at lowtemperatures ranging from -100 to 0 C can be given by [9,12] :๐๐๐๐ ๐ถ1๐ ๐ถ2 ๐ถ3 ๐ ๐ถ4 ๐ 2 ๐ถ5 ๐ 3 ๐ถ6 ๐ 4 ๐ถ7 ๐๐๐(10)where๐ถ1 -5.6745359 103๐ถ2 6.3925247๐ถ3 -9.677843 10-3๐ถ4 6.2215701 10-7๐ถ5 2.0747825 10-9๐ถ6 -9.484024 10-13๐ถ7 4.1635019Comparison between these values (from Appendix 6.3) shows excellent agreement of thecorrelation values with accurate ASHRAE data, with an absolute deviation lying between0.000213 % to 0.307013 %. This infers that this correlation is reliable, which will rendersimple computations over importing the data from tables (ASHRAE) to the program. Thiscould also be used when the range of dry bulb temperatures are huge to be imported fromtables.
4NUMERICAL CODEContruction Psychor chart MATLAB.mThe numerical code developed in MATLAB to generate the psychrometric chart is shownbelow. The line colours, line widths and additional text were added on the plot to make it userfriendly. Comments are also shown to explain the significance of each line in the code.%Program to plot a low temperature simplified psychrometric chart%% Section to plot the saturation line of 100% RHclc;clear all;format longprop xlsread('Thermodynamic prop.xlsx'); %reading thermodynamic propertiesfrom excel filet a prop(:,1); %dry bulb temperature (deg C)p s prop(:,2); %saturated vapour pressure (kN/m 2)v sp prop(:,3); %specific volume of moist air (m 3/kg)h f prop(:,4); %enthalpy of saturated water (kJ/kg)w s (0.62198*p s*1000)/(101325-(1000*p s)); %saturated specific humidityw s w s(:,1);figure(1);plot(t a,w s,'Color',[0 0.5 0],'LineWidth',2); %plotting saturation line of100% RH - Greengrid on;grid minor;axis([-60 0 0 2.5e-3]);xlabel('Dry bulb temperature (deg C)','FontSize',12,'FontName','Times NewRoman','FontWeight','bold');ylabel('Specific Humidity (kg/kg)','FontSize',12,'FontName','Times ion','right');title('Plot of saturation line','FontSize',15,'FontName','Times turation Line','-djpeg','-r300');figure(6);% figure('units','inches');% set(gcf,'pos',[1 1 1366 608])fullfig(figure(6));plot(t a,w s,'Color',[0 0.5 0],'LineWidth',2); %plotting saturation line of100% RH - Greenhold on; %holds the figure for plotting next portionsgrid on; %plotting grid linesgrid minor;xlabel('Dry bulb temperature (deg C)','FontSize',12,'FontName','Times NewRoman','FontWeight','bold');ylabel('Specific Humidity (kg/kg)','FontSize',12,'FontName','Times ion','right');title('Psychrometric chart','FontSize',15,'FontName','Times NewRoman','FontWeight','bold');axis([-65 0 0 2.5e-3]); %limits of x- and y-axis%% Section to plot constant RH linesfor rh 0.1:0.1:0.9 %varying rh from 10% to 90%p v rh*p s; %vapour pressurew (0.62198*p v*1000)/(101325-(1000*p v)); %specific humidity at aconstant RH
figure(2);plot(t a,w,'g-','Color',[0 0.5 0],'LineWidth',2); %plotting constant RHlines from 10% to 90% RH - Greengrid on;grid minor;axis([-60 0 0 2.5e-3]);xlabel('Dry bulb temperature (deg C)','FontSize',12,'FontName','TimesNew Roman','FontWeight','bold');ylabel('Specific Humidity (kg/kg)','FontSize',12,'FontName','Times ion','right');title('Plot of Constant RH lines','FontSize',15,'FontName','Times NewRoman','FontWeight','bold');hold on;figure(6);plot(t a,w,'g-','Color',[0 0.5 0]); %plotting constant RH lines from10% to 90% RH - Greengrid on;grid minor;hold ;print(figure(2),'Constant RH ,'10%','Color',[0 0.5 0]);text(-5,0.5e-3,'20%','Color',[0 0.5 0]);text(-6,0.7e-3,'30%','Color',[0 0.5 0]);text(-9,0.9e-3,'50%','Color',[0 0.5 0]);text(-11,1.1e-3,'70%','Color',[0 0.5 0]);text(-12,1.3e-3,'90%','Color',[0 0.5 0]);%% Section to plot constant volume lines%adopting an iterative procedurefor v sq 0.61:0.01:0.77 %varying vol. from 0.61 m 3/kg to 0.77 m 3/kgt s0 interp1(v sp,t a,v sq); %guessed (interpolated) value of satd.tempdiff 1.0; %assumed differencewhile diff 3e-6p s0 interp1(t a,p s,t s0); %value of satd. pressure at that satd.temp (interpolated)v s0 (287.1*(t s0 273.15))/(101325-(1000*p s0)); %recalc. sp.volumediff abs(v s0-v sq); %absolute error b/w true sp. volume andapprox. oneif diff 3e-6break;elseif v s0 v sqt s0 t s0-0.001; %decrementing satd. tempcontinue;elset s0 t s0 0.001; %incrementing satd. tempcontinue; %continues the loopendendw sp 0.62198*(1000*p s0)/(101325-(1000*p s0)); %satd. humidity atconst. volume
t 0 (101325*v sq)/287.3-273.15; %temp at 0 humidity along the const.sp. volume linefigure(3);plot([t s0,t 0],[w sp,0],'b-','LineWidth',2); %plotting constant volumelinesgrid on;grid minor;axis([-60 0 0 3.5e-3]);xlabel('Dry bulb temperature (deg C)','FontSize',12,'FontName','TimesNew Roman','FontWeight','bold');ylabel('Specific Humidity (kg/kg)','FontSize',12,'FontName','Times ion','right');title('Plot of Constant specific volumelines','FontSize',15,'FontName','Times New Roman','FontWeight','bold');hold on;figure(6);plot([t s0,t 0],[w sp,0],'b-','LineWidth',2); %plotting constant volumelineshold on;grid on;grid minor;endfigure(3);text(-6,3.1e-3,'0.77 m 3/kg');text(-7,2.5e-3,'0.76 m 3/kg');text(-11,2e-3,'0.75 m 3/kg');text(-14,1.4e-3,'0.74 m 3/kg');text(-18,1e-3,'0.73 m 3/kg');text(-25,0.5e-3,'0.71 m 3/kg');text(-32,0.4e-3,'0.69 m 3/kg');text(-40,0.2e-3,'0.67 m 3/kg');text(-46,0.1e-3,'0.65 m 3/kg');text(-58,0.08e-3,'0.61 m 3/kg');print(figure(3),'Constant specific volume .77 m 3/kg','rotation',90,'Color',[0 otation',90,'Color',[0 0 otation',90,'Color',[0 0 tion',90,'Color',[0 0 rotation',90,'Color',[0 otation',90,'Color',[0 0 otation',90,'Color',[0 0 1],'FontWeight','bold');%% Section to plot constant WBT linesfor t s0 -60:0 %varying satd. dbt from -60 to 0h fs interp1(t a,h f,t s0); %interpolated enthalpy of satd. water fromtablesp s0 interp1(t a,p s,t s0); %interpolated satd. vap pressurew s0 0.62198*(1000*p s0)/(101325-(1000*p s0)); %satd. humidityh s0 (1.006 1.805*w s0)*t s0 (2501*w s0); %satd. humidity alongconstant WBT linesigma fn h s0-(w s0*h fs); %calc. sigma heat functiont 0 sigma fn/1.006; %temp at 0 humidity along constant WBT linefigure(4);plot([t s0,t 0],[w s0,0],'r-','LineWidth',2); %plot the linehold on;grid on;grid minor;axis([-60 0 0 2.5e-3]);
xlabel('Dry bulb temperature (deg C)','FontSize',12,'FontName','TimesNew Roman','FontWeight','bold');ylabel('Specific Humidity (kg/kg)','FontSize',12,'FontName','Times ion','right');title('Plot of Constant WBT lines','FontSize',15,'FontName','Times NewRoman','FontWeight','bold');figure(6);plot([t s0,t 0],[w s0,0],'r-'); %plot the linegrid on;grid minor;hold on;endprint(figure(4),'Constant WBT lines','-djpeg','-r300');%% Section to plot constant enthalpy lines (rather than enthalpy deviation)for h -60:5 %range of enthalpy variationt 0 h/1.006; %temp at 0 humidity along constant enthalpy linep [8.1225e-5 1.12387 7.377795-h]; %polynomial(enthalpy) as a functionof dbtt roots(p); %finding the roots of the above polynomialif(t(1) 0 && t(1) -60) %only the temp. which lies in this range isreliablet1 t(1);elset1 t(2);endw1 4.5e-5*t1 2.95e-3; %enthalpy axis eqn.figure(5);if rem(h,5) 0 %solid lines for enthalpies which are multiples of 5plot([t 0,t1],[0,w1],'k-','LineWidth',2);elseplot([t 0,t1],[0,w1],'k--'); %dashed linesendgrid on;grid minor;axis([-65 0 0 2.5e-3]);xlabel('Dry bulb temperature (deg C)','FontSize',12,'FontName','TimesNew Roman','FontWeight','bold');ylabel('Specific Humidity (kg/kg)','FontSize',12,'FontName','Times ion','right');title('Plot of Constant Enthalpy lines','FontSize',15,'FontName','TimesNew Roman','FontWeight','bold');hold on;figure(6);if rem(h,5) 0 %solid lines for enthalpies which are multiples of 5plot([t 0,t1],[0,w1],'k-','LineWidth',2);elseplot([t 0,t1],[0,w1],'k--'); %dashed linesendgrid on;grid minor;hold on;endfigure(5);plot([-60 -10],[0.25e-3 2.5e-3],'k-','LineWidth',2); %plotting the anthalpyaxistext(-65,0.35e-3,'-60 50');text(-49,0.9e-3,'-45');
2.3e-3,'-10');print(figure(5),'Constant Enthalpy line','-djpeg','-r300');figure(6);plot([-60 -10],[0.25e-3 2.5e-3],'k-','LineWidth',2); %plotting the anthalpyaxistext(-62,0.35e-3,'-60 ,'rotation',23);text(-35,0.0018,'Enthalpy (kJ/kg) 6.1,0.57e-3,'Wet Bulb and Dew Point or ion',40);hold on;%% Section to plot the SHF protractor% x0 -54; %positions at which the SHF protractor is drawn from% y0 2.25e-3;% for shf 0.9:-0.1:0.2 %left half portion of shf%delta t 4.0; %assuming temp. diff.%delta w (1.0216*delta t/2501)*(1/shf-1); %calc. sp. humidity diff.%x1 x0-5.0*(5.0-delta t); %end points of the shf line%y1 y0-delta w;%figure(6);%plot([x0 x1],[y0 y1],'k-'); %plotting the shf line%hold on;% end% for shf 1.1:0.1:4.0 %right half portion of shf%delta t 4.0;%delta w (1.0216*delta t/2501)*(1/shf-1);%x2 x0 5.0*(5.0-delta t);%y2 y0 delta w;%figure(6);%plot([x2 x0],[y2 y0],'k-');%hold on;% 372 0.767034774436087 ,.'Color',[0.235294118523598 0.235294118523598 .213762811127379 0.315519765739385],.[0.844888529167162 .262811127379209 0.218887262079063],.[0.841105263157894 .262811127379209 0.232064421669107],.[0.84375 .264275256222548 0.243045387994143],.[0.841105263157894 0.773026315789473]);
annotation(figure(6),'line',[0.262811127379209 0.248901903367496],.[0.841105263157894 .262811127379209 0.253294289897511],.[0.837815789473684 .262811127379209 0.256954612005857],.[0.841105263157894 .263543191800879 0.311127379209371],.[0.84275 .265007320644217 0.304538799414348],.[0.839460526315789 .262811127379209 0.293557833089312],.[0.842105263157895 .264275256222548 0.288433382137628],.[0.839460526315789 .263543191800879 0.281844802342606],.[0.839460526315789 .263543191800879 0.27598828696
known. Since the psychrometric chart is constructed at constant atmospheric pressure, any two independent variables in the psychrometric chart can help one in locating other properties too. This is the basic principle adopted in the current study. 2.1 Saturation Line All the points on the saturated line correspond to a Relative Humidity of 100%.
temperature sensors. The LogTag Temperature Data Logger measures and stores up to 7770 temperature readings over -40 C to 99 C (-40 F to 210 F) measurement range from a remote temperature probe. Statistical temperature and duration readings for up to 30 days can be reviewed on the display. The visual display of current temperature
46-47ow Temperature (R-448A/R-449A)L 48-49ow Temperature (R-407A/R-407F)L 50-51ow Temperature (R-407C)L 52 Unit Specifications 53 Electrical Data 53 Medium and Low Temperature Semi-Hermetic Models 54WEF Medium Temperature Data A 55WEF Low Temperature Data A Replacement Parts Dimensional Diagrams
akuntansi musyarakah (sak no 106) Ayat tentang Musyarakah (Q.S. 39; 29) ูููููุฒ รฃู รฅูุงู รณู รฎูุฎุธูู รณ รูู รซ รูุฌูุฒูู ร ุง รคููู ร ูุท ููููุฌูุฑู รญู รฅู รฎุธูู รุงูุด
Collectively make tawbah to Allฤh S so that you may acquire falฤแธฅ [of this world and the Hereafter]. (24:31) The one who repents also becomes the beloved of Allฤh S, รูู รู๏บุง๏ปฎูู๏บ๏ปุงูู๏บูู รูู รง๏ปชูููฐ๏ป ๏ปุงูููุงู Verily, Allฤh S loves those who are most repenting. (2:22
the same refrigerant moving between the low and medium-temperature compressors. The low-temperature compressors discharge to the suction of the medium-temperature compressors. In other words, the medium-temp compressors serve as a booster to the low-temp compressors. Suction gas from the low-temperature display case and freezer evaporators .
Complete one map together using the following directions. 8. Find the low point and the high temperature reading. Label the L for low and the high temperature H. 9. Subtract the value of the low from the high reading to determine an easy interval. 10. Work from the low temperature reading to the high temperature reading. Choose the most even .
7.According to Reference Table G, how many grams of KNO3 would be needed to saturate 200 grams of water at 70ยบC? A)high pressure and low temperature B)high pressure and high temperature C)low pressure and low temperature D)low pressure and high temperature 8.Carbon dioxide gas is most soluble in water under conditions of A)10.ยบC B)20.ยบC C)30 .
4.3.1 Effect of Temperature at pH 4.5 57 4.3.2 Effect of Temperature at pH 5.0 58 4.3.3 Effect of Temperature at pH 5.5 59 4.3.4 Effect of Temperature at pH 6.0 60 4.3.5 Effect of Temperature at pH 6.5 61 4.3.6 Combination Effect of Temperature on Enzymatic Hydrolysis 62
