Question

A space shuttle moves through the atmosphere on its return from space. At point 1 on its wing, the air temperature and pressure are measured to be T1 = 300°C and p1 = 10,000 Pa while at point 2 they are T, = 700°C and p2 = 575,000 Pa. Calculate the air density in kg/m3 at both points 1 and 2.

Answer 1

The air density in at points 1 is
`60.7 kg/m^3` and 2 is
`2060 kg/m^3`.

Step-by-step explanation:

Average molecular weight of an air ,M= 28.97 g/mol

`PV=nRT`

or
`PM=dRT`

P = Pressure of the gas

n = moles of gas

T = Temperature of the gas

d = Density of the gas

M = molar mass of the gas

R = universal gas constant

Density at point-1 =
`d_1`

`P_1 = 10,000 Pa=0.0986 atm`

`1 Pa=9.86923* 10^(-6) atm`

`T_1 = 300^oC = 573.15 K`

M = 28.97 g/mol

`d_1=(PM)/(RT)=(0.0986 atm* 28.97 g/mol)/(0.0821 atm L/ mol K* 573.15 K)`

`d_1 =0.0607 g/ml`

1 g = 0.001 kg

`1 mL = 10^(-6) m^3`

`d_1=(0.0607* 0.001 kg)/(10^(-6) m^3)=60.7 kg/m^3`

Density at point-2 =
`d_2`

`P_2 = 575,000 Pa=5.67 atm`

`T_2 = 700^oC = 973.15 K`

M = 28.97 g/mol

`d_2=(PM)/(RT)=(5.67 atm* 28.97 g/mol)/(0.0821 atm L/ mol K* 973.15 K)`

`d_2 =2.06 g/ml=2060 kg/m^3`