Answer
$\Delta V_{real}=0.07128m^3$
$\Delta V=0.07m^3$ $(1.80\% Error)$
Work Step by Step
From table A-6:
$\upsilon_{1}=1.31623\frac{m^3}{kg}$
$\upsilon_{2}=0.95986\frac{m^3}{kg}$
$\Delta V_{real}=m\Delta \upsilon=0.2kg*(1.31623\frac{m^3}{kg}-0.95986\frac{m^3}{kg})=0.07128m^3$
Using the compressibility factor:
$P_{R,1}=P_{R,2}=\frac{0.2MPa}{22.06MPa}=0.0091$
$T_{R,1}=\frac{(300+273.15)K}{647.1K}=0.886$
$T_{R,2}=\frac{(150+273.15)K}{647.1K}=0.654$
From compressibility chart:
$Z_{1}=0.9956$
$Z_{2}=0.9897$
$V_{1}=\frac{Z_{1}mRT_{1}}{P_{1}}=\frac{0.9956*0.2kg*0.4615\frac{kPam^3}{kgK}*(300+273.15)K}{200kPa}=0.2633m^3$
$V_{2}=\frac{Z_{2}mRT_{2}}{P_{2}}=\frac{0.9897*0.2kg*0.4615\frac{kPam^3}{kgK}*(150+273.15)K}{200kPa}=0.1933m^3$
$\Delta V=0.2633m^3-0.1933m^3=0.07m^3$ $(1.80\% Error)$
