Question

Extract from Table A-6 the values of the specific volume as function of pressure from 0.01 to 60 MPa at the maximum temperature reported (1300 °C) and compare them with the corresponding specific volumes calculated using the equation of state for an ideal gas (consider water as an ideal gas with k=1.33 and Mmol=18 g/s). Make the comparison by plotting (using Matlab or other software, no hand sketching) the percentage difference between the two sets of values as function of pressure. What is the maximum error and at what pressure occurs? Repeat the same procedure above for a temperature of 600 °C.

Answer 1

Maximum Percentage Error at 1300^oC = 0.84 %

Pressure at which maximum error occurs = 60 MPa

Maximum Percentage Error at 600^oC = 39.08 %

Pressure at which maximum error occurs = 60 MPa

MatLab Code

clear all; close all; cld co JOUWNE II III R = 8314/18; Gas constant for water in kJ/kg.k P = [0.01, 0.05, 0.1:0.1:0.6, 0.8:0.2:2.0, 2.5:0.5:5.0, 6.0:1:10.0, 12.5:2.5:20.0, 25:5:40, 50, 60); Pressure Vector in MPa

$To Plot percentage error at 1300C T1 = 1573.15; $Temperature in K $Actual specific volume at 1300C. va 1300 = [72.604, 14.5209, 7.2605, 3.63026, 2.42019, 1.81516, 1.45214, 1.21012, 0.90761, 0.72610, 0.60509, 0.51866, ... 0.45383, 0.40341, 0.36308, 0.29048, 0.24207, 0.20750, 0.18157, 0.16140, 0.14527, 0.12107, 0.103781, 0.090817, ... 0.080733, 0.072667, 0.058147, 0.048469, 0.041556, 0.036371, 0.029115, 0.024279, 0.020827, 0.018239, 0.014620, 0.012213]; vi_1300 = (R*T1)./(P*10^6); Specific volume using ideal gas equation. perc_err_1300 = abs((va_1300-vi_1300)./va_1300) *100; Absolute percentage error. [C1,11] = max (perc_err_1300); $To find the maximum absolute percentage error and corresponding vector index fprintf("Maximum percentage error (T=1300) : $d \n', ci); $To show the maximum percentage error fprintf('Pressure at which max error occurs (T=1300): $d MPa \n\n', P(11)); $To show the pressure at which maximum error occurs IIIIII $ To plot percentage error vs Pressure at 1300 figure () plot (P, perc_err_1300); xlabel('Pressure (MPa)'); ylabel('Absolute Percentage error'); title('I = 1300“C'); grid on

$To Plot percentage error at 600C or 873.15 K 37 - T2 = 873.15; $Temperature in K Actual specific volume at 600 C va_600 = [40.296, 8.0577, 4.0279, 2.01302, 1.34139, 1.00558, 0.80409, 0.66976, 0.50186, 0.40111, 0.33395, ... 0.28597, 0.24999, 0.22200, 0.19962, 0.15931, 0.13245, 0.11325, 0.09886, 0.08766, 0.07870, 0.06527, 0.055665,... 0.048463, 0.042861, 0.038378, 0.030306, 0.024921, 0.021073, 0.018185, 0.014140, 0.011445, 0.009523, 0.008089 0.006108, 0.004833]; vi_600 = (R*T2)./(P*10^6); $ perc_err_600 =abs((va_600-vi_600)./va_600)*100; $ Specific volume calculated using ideal gas equation. [C2,12] = max (perc_err_600); $To find the maximum absolute percentage error fprintf("Maximum percentage error (T=600) : %d\n', C2); fprintf("Pressure at which max error occurs (T=600): $d MPa \n', P(12)); To plot percentage error vs Pressure at 600 figure () plot(P, perc_err_600); xlabel('Pressure (MPa)'); ylabel ('Absolute Percentage error'); title('T = 600~OC'); grid on

Output

Maximum percentage error (T=1300) : 8.405653e-01 Pressure at which max error occurs (T-1300): 60 MPa Maximum percentage error (T=600) : 3.907797e+01 Pressure at which max error occurs (T=600): 60 MPa

T= 1300°C Absolute Percentage error 40 40 50 30 Pressure (MPa)

T = 600°C Absolute Percentage error 4050 30 Pressure (MPa)