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

Answer:

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

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 = $d_1$

$P_1 = 10,000 Pa=0.0986 atm$

$1 Pa=9.86923\times 10^{-6} atm$

$T_1 = 300^oC = 573.15 K$

M = 28.97 g/mol

$d_1=\frac{PM}{RT}=\frac{0.0986 atm\times 28.97 g/mol}{0.0821 atm L/ mol K\times 573.15 K}$

$d_1 =0.0607 g/ml$

1 g = 0.001 kg

$1 mL = 10^{-6} m^3$

$d_1=\frac{0.0607\times 0.001 kg}{10^{-6} m^3}=60.7 kg/m^3$

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

$d_2=\frac{PM}{RT}=\frac{5.67 atm\times 28.97 g/mol}{0.0821 atm L/ mol K\times 973.15 K}$

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