Thermodynamics

352 | ThermodynamicsEXAMPLE 7–7Effect of Density of a Liquid on EntropyLiquid methane is commonly used in various cryogenic applications. Thecritical temperature of methane is 191 K (or 82°C), and thus methanemust be maintained below 191 K to keep it in liquid phase. The propertiesof liquid methane at various temperatures and pressures are given in Table7–1. Determine the entropy change of liquid methane as it undergoes aprocess from 110 K and 1 MPa to 120 K and 5 MPa (a) using tabulatedproperties and (b) approximating liquid methane as an incompressible substance.What is the error involved in the latter case?MethanepumpP 1 = 1 MPaT 1 = 110 KP 2 = 5 MPaT 2 = 120 KHeatFIGURE 7–29Schematic for Example 7–7.Solution Liquid methane undergoes a process between two specifiedstates. The entropy change of methane is to be determined by using actualdata and by assuming methane to be incompressible.Analysis (a) We consider a unit mass of liquid methane (Fig. 7–29). Theproperties of the methane at the initial and final states areState 1:State 2:Therefore,(b) Approximating liquid methane as an incompressible substance, itsentropy change is determined to besince¢s s 2 s 1 5.145 4.875 0.270 kJ/kg # KT 2¢s c avg ln 13.4785 kJ>kg #120 KK2 lnT 1 110 K 0.303 kJ /kg # Kc avg c p1 c p22P 1 1 MPaT 1 110 K f s 1 4.875 kJ>kg # Kc p1 3.471 kJ>kg # KP 2 5 MPaT 2 120 K f s 2 5.145 kJ>kg # Kc p2 3.486 kJ>kg # K3.471 3.4862 3.4785 kJ>kg # KTABLE 7–1Properties of liquid methaneSpecificTemp., Pressure, Density, Enthalpy, Entropy, heat,T, K P, MPa r, kg/m 3 h, kJ/kg s, kJ/kg · K c p , kJ/kg · K110 0.5 425.3 208.3 4.878 3.4761.0 425.8 209.0 4.875 3.4712.0 426.6 210.5 4.867 3.4605.0 429.1 215.0 4.844 3.432120 0.5 410.4 243.4 5.185 3.5511.0 411.0 244.1 5.180 3.5432.0 412.0 245.4 5.171 3.5285.0 415.2 249.6 5.145 3.486