Question

What is the density of air at 75 °F and 1atm pressure? Express in lbm/ft³ and kg/m³.

Answer 1

For imperial value:

$T = 75^{\circ}F = (75+460) R = 535\;\;R$

and

Now, for air;

Now, by ideal gas equation;

$P = \left ( \frac{m}{V} \right ) RT$

$\Rightarrow P = \rho RT$

$\Rightarrow \rho = \frac{P}{RT}$

$\Rightarrow \rho = \frac{14.7}{0.3704(535)}$

$\Rightarrow \rho =0.074181\;\;lbm/ft^3$

...(Answer)

For SI unit:

$T = 75^oF = \left [(75-32)\times \frac{5}{9} \right ]^oC= 23.889^oC = (23.889+273)K$

$\Rightarrow T =296.889\;\;K$

and

Now, for air;

Density will be;

$\rho = \frac{P}{RT}$

$\Rightarrow \rho = \frac{101.325}{0.287(296.889)}$

$\Rightarrow \rho = 1.189\;\;kg/m^3$

...(Answer)