Answer to Question #144737 in Molecular Physics | Thermodynamics for MKHUSELI

Question

The volume of air at a pressure of 5 bar and at a temperature of 470^o C is 0.5 m³. Calculate the mass of the air, and the gas constant. The universal gas constant is 8.315kJ/kg K.

Answer 1

$$PV= nRT$$

also $PV= \frac{mass}{m.mass}\cdot RT$

molar mass(air) = 0.029kg/mol

P= pressure= 5 Bar = 500000N/m²

V= volume = 0.5m³

T= Temperature= 470⁰ C = 470 + 273= 743K

R= universal gas constant= 8.315kJ/kg

$500000\times0.5 = n\times 8.315\times743$

$n$ = $\frac{500000\times0.5}{8.315\times743}$ mol

= 40.466mol

$n=\frac{mass}{molar. mass}$

40.466$=\frac{mass}{0.029}$

mass $\approx$ 1.174Kg

Gas constant of air

$Gas constant = \frac{universal \hspace{0.05cm}gas\hspace{0.05cm}constant}{m.mass}$

$gas\hspace{0.05cm}constant = \frac{8.315}{0.029}$

$gas constant = 287J/Kg\cdot K$