Question

Determine the mass and specific volume of argon gas in a vessel at 150 kPa and 20°C vessel is spherical and has a radius of 5m.

Answer 1

The volume of the sphere is

$\displaystyle V= \frac{4}{3} \pi r^3$

$P =150 \cdot 10^3 \; Pa, \; \; T=293 K$

Using the ideal gas equation,

$\displaystyle PV = nRT = \frac{m}{M} RT$

1) mass

$\displaystyle m = \frac{PVM}{RT} = \frac{150\cdot 10^3 \cdot 1.333 \cdot 3.14 \cdot 5^3 \cdot 40 \cdot 10^{-3}}{8.31 \cdot 293}= 1289.9 \; kg \approx 1290 \;kg$

2) specific volume

$\displaystyle v = \frac{V}{m} = \frac{1.333 \cdot 3.14 \cdot 5^3}{1290} =0.405 \; m^3/kg$