Conceptual and numerical question for thermodynamics (2nd yr B.Tech mech student)

Thermodynamics Tute sheet -7

(the question in this tutorial sheet are from VAn wylen )

Real and Ideal Gases

QNo.1 A cylinder fitted with a frictionless piston contains butane at 25°C, 500kPa. Can the butane reasonably be assumed to behave as an ideal gas at this state?

QNo.2 A cylindrical gas tank 1m long, with inside diameter of 20 cm, is evacuated and then filled with CO₂ gas at 25°C. To what pressure should it be charged if there should be 1.2 kg of CO₂.                                         (2152kPa)

QNo.3 What is the percent error in specific volume if the ideal-gas model is used to represent the behaviour of superheated ammonia at 40°C and 500kPa? What if the generalized compressibility chart is used instead?                                                                                                                                                                        (4.5%,1.4%)  

QNo.4 Refrigerant R-32 is at -10°C with a quality 15%. Find the pressure and specific volume.                                                                                                                                                                            (925kPa, 0.007m³/kg)

QNo.5 Show that the van der Waals equation can be written as a cubic equation in the compressibility factor involving the reduced pressure and reduced temperature as –

                  Z³-(P_r/8T_r+1) Z² + (27P_r/64T_r²) Z - 27 P²_r/512 T³_r =0

QNo.6 One early attempt to improve on the van der Waals equation of state was an expression of the form

 P = (RT/ ʋ-b) – a/ ʋ²T, solve for the constants a,b, and ʋ_c  using the same procedure as for the van der Waals         equation.

QNo.7 A gas mixture at 120°C and 125kPa is 50% N₂, 30% H₂O and 20% O₂ on a mole basis. Find the mass fractions, the mixture gas constant, and the volume for 5kg of mixture.                                                                                                                                                                   (0.5427, 0.2094, 0.2479 ; 0.3221 kJ/kg K; 5.065 m³.)

 QNo.8 A new refrigant R-407 is a mixture of 23% R-32, 25%  R-125, and 52% R-134a on a mass basis. Find the mole fractions, the mixture gas constant and the mixture heat capacities for this new refrigerant.                                                                                       (0.381,0.180,0.439; 0.09645 kJ/kgK; 0.8298kJ/kg K; 0.7334kJ/kg K.)

QNo.9 A rigid insulated vessel contains 12 kg of oxygen at 200kPa and 280K separated by a membrane from 26kg of carbon dioxide at 400kPa and 360K. The membrane is removed, and the mixture comes to a uniform state. Find the final temperature and pressure of the mixture.                                         334.5K; 305.7kPa

QNo.10 An insulated gas turbine receives a mixture of 10% CO_2, 10% H₂O, and 80% N₂ on a mass basis at 1000K and 500 kPa. The inlet volume flow rate is 2m³/s, and the exhaust is at 700kPa. Find the power output in kW using constant specific heat from the table A.5 (or other relevant table) at 300K .             (1096 kW)

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