At an altitude of 11,000 m (a typical cruising altitude for a jet airliner), the air temperature is -56.5°C and the air density is 0.364 kg/m3 .What is the pressure of the atmosphere at that altitude? (?Note: ?The temperature at this altitude is not the same as at the surface of the earth, so the calculation of Example 18.4 in Section 18.1 doesn’t apply.)
Solution 21E To calculate the pressure of the atmosphere at the given altitude, we shall have to use the ideal gas equation PV = nRT , where P= pressure, V= volume, n= number of moles, R =gas constant and T= absolute temperature. 0 Given that, T = 56.5 = 273.15 56.5 K = 216,65 K 3 Density d = 0.364 kg/m Molar mass of air M = 0.029 kg/moles From the ideal gas equation, PV = nRT PV = w RT , w is the mass of the gas, M is the molar mass of the same M w PM = V RT w Now, V = density = d Therefore, PM = dRT …..(1) Substituting d, T and M values from above, we get 3 P × 0.029 kg/moles = 0.364 kg/m × 8.314 J/mol.K × 216.65 K 655.64 P = 0.029Pa P = 22608 Pa P = 226085 atm ( since 1 atm = 1.013 × 10 Pa) 1.013×10 P = 0.22 atm Therefore, the pressure of atmosphere at the given altitude is approximately 0.22 atm.
