Question

1. The density of air is to be determined by measuring pressure and temperature for insertion in the ideal-gas equation: p=pRT The value of R for air is 287.1 J/kg-K and may be assumed to be exact for this calculation. The temperature and pressure are measured as T = 55 +0.4°C p=125 +0.5 kPa Determine the nominal value for density in kg/m' and its uncertainty using Post Sum square a). rss (p = 1.327 +0.0055 kg/m) b). maximum error (p = 1.327 +0.00693 kg/m)

Please show all work. correct answers to a and b are in parenthesis. Thanks!

Answer 1

The given formula is P = ρRT

Where P = given pressure = 125 ± 0.5 kPa

We know 1 kPa = 1000 Pa

Then 125 ± 0.5 kPa = (125 ± 0.5) * 1000 = 12500 ± 50 Pa

R = Gas constant = 287.1 J/ kg * ^oK

T = given temperature = 55 ± 0.4 ^oC = 55 ± 0.4 + 273 = 328 0.4 ^oK

Then putting the values-

P = ρRT

ρ = P/RT

ρ = 12500 ± 50 Pa / (287.1 J/ kg * ^oK * 328 ± 0.4 ^oK)

We know 1 Pa = 1 Kg m/s²

ρ = 12500 ± 50 Kg m/s² / ( 94200 ± 110 J/kg )

Again 1 J = 1 kg m²/s².

Then

ρ = 12500 ± 50 Kg m/s² / ( 94200 ± 110 J/kg )

ρ = 12500 ± 50 Kg m/s² / ( 94200 ± 110 kg m²/s²./kg )

= 12500 ± 50 Kg m/s² / ( 94200 ± 110 m²/s²)

= 1.327 ± 0.0055 Kg/m³