Answer:
The air density in at points 1 is [tex]60.7 kg/m^3[/tex] and 2 is [tex]2060 kg/m^3[/tex].
Explanation:
Average molecular weight of an air ,M= 28.97 g/mol
[tex]PV=nRT[/tex]
or [tex] PM=dRT[/tex]
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 = [tex]d_1[/tex]
[tex]P_1 = 10,000 Pa=0.0986 atm[/tex]
[tex]1 Pa=9.86923\times 10^{-6} atm[/tex]
[tex]T_1 = 300^oC = 573.15 K[/tex]
M = 28.97 g/mol
[tex]d_1=\frac{PM}{RT}=\frac{0.0986 atm\times 28.97 g/mol}{0.0821 atm L/ mol K\times 573.15 K}[/tex]
[tex]d_1 =0.0607 g/ml[/tex]
1 g = 0.001 kg
[tex]1 mL = 10^{-6} m^3[/tex]
[tex]d_1=\frac{0.0607\times 0.001 kg}{10^{-6} m^3}=60.7 kg/m^3[/tex]
Density at point-2 = [tex]d_2[/tex]
[tex]P_2 = 575,000 Pa=5.67 atm[/tex]
[tex]T_2 = 700^oC = 973.15 K[/tex]
M = 28.97 g/mol
[tex]d_2=\frac{PM}{RT}=\frac{5.67 atm\times 28.97 g/mol}{0.0821 atm L/ mol K\times 973.15 K}[/tex]
[tex]d_2 =2.06 g/ml=2060 kg/m^3[/tex]
