Respuesta :
Answer : The density of air in [tex]lbm/ft^3[/tex] and [tex]kg/m^3[/tex] is, [tex]0.0743lbm/ft^3[/tex] and [tex]1.19kg/m^3[/tex] respectively.
Explanation :
[tex]PV=nRT\\\\PV=\frac{m}{M}RT\\\\P=\frac{m}{V}\frac{RT}{M}\\\\P=\rho \frac{RT}{M}\\\\\rho=\frac{PM}{RT}[/tex]
where,
P = pressure of air = 1 atm
V = volume of air
T = temperature of air = 297 K
The conversion used for the temperature from Fahrenheit to degree Celsius is:
[tex]^oC=(^oF-32)\times \frac{5}{9}[/tex]
[tex]^oC=(75-32)\times \frac{5}{9}=24^oC[/tex]
The conversion used for the temperature from degree Celsius to Kelvin is:
[tex]K=273+^oC[/tex]
[tex]K=273+24=297K[/tex]
n = number of moles
m = mass of air
M = average molar mass of air = 28.97 g/mole
[tex]\rho[/tex] = density of air = ?
R = gas constant = 0.0821 L.atm/mol.K
Now put all the given values in the above formula, we get:
[tex]\rho=\frac{PM}{RT}[/tex]
[tex]\rho=\frac{(1atm)\times (28.97g/mole)}{(0.0821L.atm/mol.K)\times (297K)}[/tex]
[tex]\rho=1.19g/L[/tex]
Now we have to calculate density in [tex]lbm/ft^3[/tex].
Conversion used :
[tex]1g/L=0.0624lbm/ft^3[/tex]
So,
[tex]1.19g/L=\frac{1.19g/L}{1g/L}\times 0.0624lbm/ft^3=0.0743lbm/ft^3[/tex]
The density of air in [tex]lbm/ft^3[/tex] is, [tex]0.0743lbm/ft^3[/tex]
Now we have to calculate density in [tex]kg/m^3[/tex].
Conversion used :
[tex]1g/L=1kg/m^3[/tex]
So,
[tex]1.19g/L=1.19kg/m^3[/tex]
The density of air in [tex]kg/m^3[/tex] is, [tex]1.19kg/m^3[/tex]
