methane (Tc =190.6 K, Pc = 4.61 x 106 Pa) is assumed to follow the vander Waals equation of state with a = 0.23003 m6 .Pa/mol2 and b = 4.31x10-5 m3 /mol. Using the GoalSeek routine in Microsoft Excel, a student finds three roots for the equation at T=165 K and P= 1.8 MPa: ( = 1637.20 mol/m3 , =13098.45 mol/m3 , and =8466.20 mol/m3 ).

at T = 165 K and P = 1.8 MPa, the root = 8466.20 mol/m3 corresponds to

(a) a supercritical fluid (b ) compressed liquid (c ) superheated vapor (d) a metastable state that can be reached in the laboratory with care (e ) an unstable state that cannot be obtained experimentally.