If air at 10 MPa and 100 C is treated as an ideal gas will t

If air at 10 MPa and -100 C is treated as an ideal gas, will the ideal gas law overestimate or underestimate the specific volume? What will be the percent error in the specific volume ?

Solution

for given 10 Mpa pressure and -100 C temperature density of air is 305.4 kg/m³

so, specific volume of air = 1/305.4 = 0.003274 m³/kg

from ideal gas law eqution PV=mRT

so specific volume from ideal gas law equation = RT/P = 287.058*173/10000000 = 0.004966 m³/kg

so ideal gas law over estimtes the specific volume of air

error percent =( (0.004966-0.003274)/0.003274)*100 = 51.683 %