Question

N10. a. What is the density of air, given P- 80 kPa and T=0°C? b. What is the temperature of air, given P-90 kPa and p 1.0 kg m-3 ? and ρ= 1.2 kg·m-3 ? C. What is the pressure of air, given T-90℉ d. Give 2 combinations of pressure and density that have a temperature of 30°C. e. Give 2 combinations of pressure and density that have a temperature of 0°C. f. Give 2 combinations of pressure and density that have a temperature of -20°C. g. How could you determine air density if you did not have a density meter? h. What is the density of air, given P - 50 kPa and T--30 °C?

Answer 1

We use standard expression for ideal gas PV = nRT doublerightarrow P = n/V RT = nM/VM RT = rho RT/M ---(1) where M is molecular weight. P = 80 times 10^3 Pa, T = 273 k = 0 degrees, M = 28.97 g/mol = 28.97 times 10^-3 kg/mol doublerightarrow Now from Eq (1) rho = PM/RT = 80 times 10^3 times 28.97 times 10^-3/8.314 times 273 = 1.02 kg/m^3 T = 90 degrees F = 305.4 k, rho = 1.2 kg m^-3 P = rho RT/M = 1.2 times 8.314 times 305.4/28.97 times 10^-3 = 105175 Pa T = ?, P = 90 times 103 Pa, rho = 1 kg m^-3 T = PM/rho R = 90 times 10^3 times 28.97 times 10^-3/1 times 8.314 = 314 k P/rho = RT/M = 8.314 times 303/28.97 times 10^-3 = 86.96 times 10^3 when rho = 1 kg/m^3, P = 86.96 times 10^3 Pa when rho = 1.1 kg/m^3, P = 96.65 times 10^3 Pa