A volume of 0.3 m3 of O2 at 200 K and 8 MPa is mixed with 0.5 m3 of N2 at the same temperature and pressure, forming a mixture at 200 K and 8 MPa. Determine the volume of the mixture, using (a) the ideal-gas equation of state, (b) Kay's rule, and (c) the compressibility chart and Amagat's law.

a) According to ideal gas equation, when two gases of V1 and V2 volumes add then we need to add the number of moles of each gas. Since in this case, pressure and temperature is same hence volumes would simply add

Volume of O2 = 0.3

Volume of N2 = 0.5

Volume of mixture = 0.3 + 0.5 = 0.8

b) According to kay's rule,

We take the portion of each gas and compute it with respect to its temperature and then add these both. In our case, since temeperature is same so volumes would simply add up

Volume of mixture = 0.8

C) According to Amagat's law,

In this case, the compressibiity factor would be unity because the temeperature of both gases and mixture is same.

Volume of mixture = 0.8