rite a Matlab function program der4(x, y) which, given the value of a function at five unequally spaced base points (x,y), uses a fourth degree Newton divided 1) W erence interrolating polynomial to return the value of the derivative of the function at the central base point. Include a hand-written write up showing the derivation of the equations used in your program Write a Matlab program which calls the function program developed in part (1) to solve the following problem: 2) Calculate the enthalpy of vaporization he of R-134a refrigerant at -32C to at least 5 significant figures from the Clapeyron equation Here (dP/dT)sat is the slope of the vaporization line, T is absolute temperature and vrg is the difference in specific volume between saturated liquid and saturated vapor (ra -v). Use appropriate data from the refrigerant R- 134a table below and compare your calculated value of hro with that reported in the table. Perform the calculation two ways: (a) Using the 5 base points closest to 32C, and (b) using the 5 equally spaced base points closest to -32 C. In each case select the base points so that there is an equal number of base points on either side ofthe central base point-32c. which result is more accurate? Saturated refrigerant-1.34a-Temperature table Specific volume m/kg Enthalpy kJ/kg Temp. Press. Sat. vapor liquid Evap. vapor 36 -32 28 -26 0 051 64 0.000 7055 0 3560 0.063 32 0.0007113 0 2947 007704 0.0007172 0 2451 0093 05 0000 7233 02052 0.10199 0.000 7265 0.1882 0.00 222 88 222 88 4.73 22067 225 40 9.52 21637 227.90 1437 216.01 230.38 682 214 80 231 62 24 -22 20 18 -16 0 111 60 0 000 729 6 0.1728 1929 213.57 232.85 0.121 92 0.000 7328 0.1590 21.77 212 32 234.08 0.132 99 0.000 7361 0.1464 24.26 211.05 235.31 0 144 83 0 000 7395 0.1350 26.77 209.76 236 53 0.157 48 0.000 7428 0 124729.30 206.45 237 74 0185 40 OCO) 7498 0.1068 3439 26.77 240 15 0.21704 0000 7569 00919 39 54 20300 242.54 0 25274 0.000 7644 0.0794 44 75 200 15 244.90 0292 82 0 000 7721 006895002 197 21 247.23 55 35 194.19 249.53 12 0 337 65 0.000 7801 0 0600 038756 0.000 7 0.504 16 0 000 8062 0.0406 7884 00525 60 73 191.07 251.80o 0 442 94 0 000 7971 0 0460 66.18 187.85 254.03 12 71.69 184.52 256 22 77 26 181.09 258 36 0 645 66 0.000 625 7 0.0317 8290 177 55 260.45 o ees 30 o.000 630 9 0 029885 75 175.73 261.48 88 61 173 89 262 50 0 77006 0 000 8417 0265 91.49 172.00 283 50 26 0.726 75 0.000 636 2 32 .815 28 0000 8473 00250 94 39 170.09 264 45 862 47 0 000 853 0 00236 97.31 168.14 26545 0 91168 0 000 859 0 0 0223100 25 166.15 266.40 0 962 98 0 000 865 1 00210 103 21 164 12 267.33 38 1 0720 0 000 8780 00188 09 19 159.94 269.14 11299 0000 8847 00177 112 22 157 79 270.01 rite a Matlab function program der4(x, y) which, given the value of a function at five unequally spaced base points (x,y), uses a fourth degree Newton divided 1) W erence interrolating polynomial to return the value of the derivative of the function at the central base point. Include a hand-written write up showing the derivation of the equations used in your program Write a Matlab program which calls the function program developed in part (1) to solve the following problem: 2) Calculate the enthalpy of vaporization he of R-134a refrigerant at -32C to at least 5 significant figures from the Clapeyron equation Here (dP/dT)sat is the slope of the vaporization line, T is absolute temperature and vrg is the difference in specific volume between saturated liquid and saturated vapor (ra -v). Use appropriate data from the refrigerant R- 134a table below and compare your calculated value of hro with that reported in the table. Perform the calculation two ways: (a) Using the 5 base points closest to 32C, and (b) using the 5 equally spaced base points closest to -32 C. In each case select the base points so that there is an equal number of base points on either side ofthe central base point-32c. which result is more accurate? Saturated refrigerant-1.34a-Temperature table Specific volume m/kg Enthalpy kJ/kg Temp. Press. Sat. vapor liquid Evap. vapor 36 -32 28 -26 0 051 64 0.000 7055 0 3560 0.063 32 0.0007113 0 2947 007704 0.0007172 0 2451 0093 05 0000 7233 02052 0.10199 0.000 7265 0.1882 0.00 222 88 222 88 4.73 22067 225 40 9.52 21637 227.90 1437 216.01 230.38 682 214 80 231 62 24 -22 20 18 -16 0 111 60 0 000 729 6 0.1728 1929 213.57 232.85 0.121 92 0.000 7328 0.1590 21.77 212 32 234.08 0.132 99 0.000 7361 0.1464 24.26 211.05 235.31 0 144 83 0 000 7395 0.1350 26.77 209.76 236 53 0.157 48 0.000 7428 0 124729.30 206.45 237 74 0185 40 OCO) 7498 0.1068 3439 26.77 240 15 0.21704 0000 7569 00919 39 54 20300 242.54 0 25274 0.000 7644 0.0794 44 75 200 15 244.90 0292 82 0 000 7721 006895002 197 21 247.23 55 35 194.19 249.53 12 0 337 65 0.000 7801 0 0600 038756 0.000 7 0.504 16 0 000 8062 0.0406 7884 00525 60 73 191.07 251.80o 0 442 94 0 000 7971 0 0460 66.18 187.85 254.03 12 71.69 184.52 256 22 77 26 181.09 258 36 0 645 66 0.000 625 7 0.0317 8290 177 55 260.45 o ees 30 o.000 630 9 0 029885 75 175.73 261.48 88 61 173 89 262 50 0 77006 0 000 8417 0265 91.49 172.00 283 50 26 0.726 75 0.000 636 2 32 .815 28 0000 8473 00250 94 39 170.09 264 45 862 47 0 000 853 0 00236 97.31 168.14 26545 0 91168 0 000 859 0 0 0223100 25 166.15 266.40 0 962 98 0 000 865 1 00210 103 21 164 12 267.33 38 1 0720 0 000 8780 00188 09 19 159.94 269.14 11299 0000 8847 00177 112 22 157 79 270.01
