Thermodynamics

830 | ThermodynamicsAssumptions 1 Carbon dioxide is an ideal gas with constant specific heatsat room temperature. 2 Flow through the duct is steady, one-dimensional,and isentropic.Properties For simplicity we use c p 0.846 kJ/kg · K and k 1.289throughout the calculations, which are the constant-pressure specific heatand specific heat ratio values of carbon dioxide at room temperature. Thegas constant of carbon dioxide is R 0.1889 kJ/kg K (Table A–2a).Analysis We note that the inlet temperature is nearly equal to the stagnationtemperature since the inlet velocity is small. The flow is isentropic, andthus the stagnation temperature and pressure throughout the duct remainconstant. Therefore,andTo illustrate the solution procedure, we calculate the desired properties atthe location where the pressure is 1200 kPa, the first location that correspondsto a pressure drop of 200 kPa.From Eq. 17–5,From Eq. 17–4,From the ideal-gas relation,From the mass flow rate relation,From Eqs. 17–11 and 17–12,1000 mc 2kRT 11.289210.1889 kJ>kg # 2 >s 2K21457 K2 a b 333.6 m>sB 1 kJ>kgMa V cT T 0 a P 1k12>kbP 0V 22c p 1T 0 T2A m#rV B2 10.846 kJ>kg # K21473 K 457 K2 a1000 m 2 >s 31 kJ>kg b 164.5 m/sr P RT 3 kg>s113.9 kg>m 3 21164.5 m>s2 13.1 104 m 2 13.1 cm 2164.5 m>s333.6 m>s 0.493T 0 T 1 200°C 473 KP 0 P 1 1400 kPa11.28912>1.2891200 kPa 1473 K2a1400 kPa b 457 K1200 kPa10.1889 kPa # m 3 >kg # K21457 K2 13.9 kg/m 3The results for the other pressure steps are summarized in Table 17–1 andare plotted in Fig. 17–13.Discussion Note that as the pressure decreases, the temperature and speedof sound decrease while the fluid velocity and Mach number increase in theflow direction. The density decreases slowly at first and rapidly later as thefluid velocity increases.