Answer
a) $\upsilon=0.0192\frac{m^3}{kg}$
b)$\upsilon=0.01536\frac{m^3}{kg}$
c)$\upsilon=0.011481\frac{m^3}{kg}$
Work Step by Step
a) Based on the ideal gas equation:
$\upsilon=\frac{RT}{P}=\frac{0.4615\frac{kPam^3}{kgK}*(350+273.15)K}{15000kPa}=0.0192\frac{m^3}{kg}$
b) Using the generalized compressibility chart:
$P_{R}=\frac{P}{P_{cr}}=\frac{10MPa}{22.06MPa}=0.453$
$T_{R}=\frac{T}{T_{cr}}=\frac{623.15K}{647.1K}=0.963$
From Fig A-15
$Z=0.8$
Then $\upsilon=Z\upsilon_{ideal}=0.8*0.0192\frac{m^3}{kg}=0.01536\frac{m^3}{kg}$
c)From table A-13E:
$\upsilon=0.011481\frac{m^3}{kg}$