Question

The density p of the air contained in a pressurized tank is to be calculated by measuring the pressure 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 for air. kg 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

500k is here, R ) Kg.k for air. Answer Given data: Uncertainty in temperature is . AT=5k Uncertainty pressure is AP=2.5x 103 Pa nominal Temperature is T = nominal is pressure P: 500x 108 Paz500000 Pa The nominal density ideal by p = equation Pv=MRT P gas or P=PRT RT Substitution , = 287 / Р 500x103 Pa Fugl р = 3.484 kg/m3 The expression for the uncertainty uncertainty in density is, AS = 3 (Att Substituting values, AS = 3.484 kg/m3 500K 287 I x 500 P ( 41+) 5K +2.5x103 Pa 500 x 103 Pa ALE = 3.484 kg/m3 X 3 200 Thus, AP = 0.0 523 kg/m3 the density is 13.484 kg/m3 and 0.0523 the uncertainty in density is kg/m3