We would like to measure the density of an ideal gas. We know the ideal gas law provides rho = P/RT, where P represents pressure, R is a constant equal to 287.058 J/kg-K and T represents temperature. We use a pressure transducer to take 15 measurements, all under the same conditions. The sample mean and standard deviation obtained from these 15 pressure measurements are 120,300 Pa and 6,600 Pa respectively. The pressure transducer specifications sheet reports an accuracy of 0.6% of the full-scale output (FSO) and a sensitivity error of 0.3% of the FSO. The FSO for this instrument is 180,000 Pa.
In addition, we use a thermocouple to measure the gas temperature. We take 20 temperature measurements and obtain a sample mean and standard deviation of 340 K and 8 K, respectively. The accuracy of the thermocouple is 0.25% of the reading and its calibration error is +_ 2 K.
1. Calculate the density of the ideal gas and its total uncertainty for a 95% probability.