Calculator 3S: Polynomial Expressions for cp for Various Gasses (SI) c = a+b+cT + dT [T in K, cp in kJ/(kmol * K)] VCR Temp. Range Error % d KJ/Kg*K Max Average Cp (300K) kJ/(kg*K) Substance Formula Search substances... a b Nitrogen N2 28.9 -0.1571 X 10-2 0.8081 X 10-5 -2.873 X 10-9 273-1800 0.59 0.34 1.0385 Oxygen Air Hydrogen 25.48 1.520 X 10-2 -0.7155 X 10-5 1.312 X 10-9 273-1800 1.19 0.28 0.9197 28.11 0.1967 X 10-2 0.4802 X 10-5 -1.966 X 10-9 273-1800 0.72 0.33 1.0097 H 29.11 -0.1916 X 10-2 0.4003 X 10-5 -0.8704 X 10-9 273-1800 1.01 0.26 14.4360 Carbon monoxide CO 28.16 0.1675 X 10-2 0.5372 X 10-5 2.222 X 10-9 273-1800 0.89 0.37 1.0431 Carbon dioxide CO2 22.26 5.981 X 10-2 -3.501 X 10-5 7.469 X 10-9 273-1800 0.67 0.22 0.8467 Temperature T Internal Energy u Enthalpy h so Table 5S: Ideal Gas Properties of Air at Low Pressure (SI) Reference Entropy* Reference Pressure* Reference Specific Volume* Specific Heat at Constant Pressure Specific Heat at Constant Volume C Ratio of Specific Heats k vo 1500 52.32 73.33 5.2906 0.0101 20488 1.0025 0.7152 1.4016 C kJ/kg kJ/kg kJ/(kg*K) kJ/(kg*K) kJ/(kg*K) Calculate 900 910.45 1247.4 8.1571 219.89 15.113 1.1706 0.8834 1.3251 950 954.81 1306.1 8.2062 260.84 13.284 1.1779 0.8907 1.3225 1000 999.52 1365.2 8.2535 307.6 11.725 1.1848 0.8976 1.32 1100 1088.6 1483 8.3436 420.98 9.24 1.1973 0.9101 1.3156 1200 1181.5 1604.6 8.4281 565.19 7.3836 1.2083 0.921 1.3118 1300 1274.1 1726 8.5078 746.01 5.9736 1.218 0.9308 1.3086 1400 1367.7 1848.2 8.5831 969.91 4.8867 1.2267 0.9395 1.3057 1500 1462 1971.3 8.6546 1244 4.0377 1.2345 0.9473 1.3032 1600 1557.1 2095.1 8.7225 1576.1 3.3666 1.2416 0.9544 1.301 Temperature Internal Energy T u Enthalpy h Table 5S: Ideal Gas Properties of Air at Low Pressure (SI) Reference Entropy* Reference Pressure* Reference Specific Volume* Specific Heat at Constant Pressure Specific Heat at Constant Volume C Ratio of Specific Heats k vo 500 52.32 73.33 5.2906 0.0101 20488 1.0025 0.7152 1.4016 C kJ/kg kJ/kg kJ/(kg*K) kJ/(kg*K) kJ/(kg*K) Calculate 350 453.36 632.34 7.4535 18.95 93.152 1.0568 0.7695 1.3732 400 492.13 685.48 7.5356 25.218 75.617 1.0687 0.7815 1.3675 450 531.51 739.22 7.6126 32.977 62.12 1.0808 0.7935 1.362 500 571.49 793.56 7.6852 42.475 51.563 1.0927 0.8054 1.3566 550 612.06 848.49 7.754 53.987 43.192 1.1042 0.817 1.3516 600 653.19 903.98 7.8195 67.812 36.475 1.1154 0.8281 1.3468 650 694.87 960.02 7.8819 84.28 31.028 1.126 0.8388 1.3424 700 737.07 1016.6 7.9415 103.75 26.571 1.136 0.8488 1.3384 750 779.75 1073.6 7.9987 126.61 22.892 1.1455 0.8583 1.3346 Input: T; Outputs: u,h,s,P,v,cp,cv,k *Please refer to Sections 6.3.1 and 6.4.1 for details on the use of s, P, and v. Table 4S: Mean Specific Heats at Constant Pressure (CP,MEAN) for Various Gasses (SI) Temperature C K Air Mean Specific Heat, kJ/(kg * K) Nitrogen Carbon Dioxide Water Vapor 1000 1273 1.0935 1.1206 1.1338 2.1485 1100 1373 1.1014 1.1301 1.1495 2.1821 1200 1473 1.1111 1.1391 1.1638 2.2151 1300 1573 1.1192 1.1475 1.1768 2.2474 1400 1673 1.1267 1.1555 1.1889 2.2788 1500 1773 1.1337 1.1629 1.1998 2.3091 1600 1873 1.1404 1.1699 1.2101 2.3385 1700 1973 1.1466 1.1765 1.2194 2.3667 1800 2073 11525 1 1827 1.2274 23939 Table 4S: Mean Specific Heats at Constant Pressure (CP.MEAN) for Various Gasses (SI) Mean Specific Heat, kJ/(kg * K) Temperature C K Air Nitrogen 25 298 1.0051 1.0403 50 323 1.0060 1.0408 Carbon Dioxide Water Vapor 0.8443 1.8644 0.8572 1.8668 100 373 1.0076 1.0415 0.8815 1.8755 200 473 1.0131 1.0447 0.9251 1.8974 300 573 1.0209 1.0505 0.9630 1.92370 400 673 1.0305 1.0586 0.9964 1.9523 500 773 1.0411 1.0682 1.0260 1.9828 600 873 1.0521 1.0787 1.0524 2.0145 700 973 1.0631 1.0895 1.0761 2.0473 17. Air enters the turbine section of a jet engine at a temperature of 1,500 C and leaves at 500 C. Compute the change in specific enthalpy (kJ/kg) through the turbine in four different ways: a. assuming constant specific heat evaluated at the entering temperature using the polynomial expressions in Table 3s b. assuming constant specific heat evaluated at the mean temperature using Table 4s c. integrating the polynomial function in Table 3s to account for variable specific heat d. using the h values tabulated in Table 5s. Compare your results for methods a, b, and c with those of method d. Do the h values in Table 5s take variable specific heat into account?