Question

Problem No. 3 (20 Points) The density p of the air contained in a pressurized tank is to be calculated by measuring the pressure P and the temperature T inside the tank. Density of the air in the tank calculated is to be from the ideal gas law: P = PRT Where R = 287 kg*K for air. The temperature is to be measured with uncertainty of 5 K. The pressure is to be measured with uncertainty of 2.5 (10) Pa. If the nominal temperature reading is 500 K and the nominal pressure is 500(10): Pa, calculate the nominal density, and the uncertainty in density calculation from the ideal gas relation. Which measurement method contributes most to the uncertainty in the density calculation?

Answer 1

Problem (3) Idean gos: P: ERT e density R: Gros constat Tz Temperature At uncertanily condition To e calculation P=eRT P=2.5x103 Pa T= 5k R = 287 lugh RT p 27 287x8 5x10² nominal condition = 500 topo @= P T= ook RT R=287 e-sooxio Soox 287 0.5742 P RT 2.5x103 @= 287x5 ez 1.7421 kg/m3 @=3.4843 kg/ons The uncertanity measurement condition is most won. Accurate aion density value From STP condition P= 105 Pa T=273.15 es P. TR e = 1.275 kglm' uncertanly value neary STP condition measurement R2287 Tends to