1. The problem statement, all variables and given/known data Calculate the percent carbon in an iron-carbon alloy that will give no volume change when liquid transforms to austenite plus graphite during solidification. 2. Relevant equations Density of liquid = 7.0 g/cc Density of austenite = 7.69 g/cc Density of graphite = 1.5 g/cc 3. The attempt at a solution For constant volume, lets say the area is 1 cubic centimeter x*(1.5 g/cc)+y*(7.69 g/cc) = (1 cc)*(7.0 g/cc) Since the volume is constant, x+y = 1 cc, and thus y = 1-x Putting it into the original equation yields: x*(1.5 g/cc) + (1-x)*(7.69 g/cc) = (1 cc)*(7.0 g/cc) Thus, x=0.111 cc, y=0.889 cc Now at this point I am confused. Since the graphite is 100% carbon, there will be 1*.111 % carbon, but what will it be for the austenite as we are not given what temperature this occurs at so that we may not see the iron-cementite phase diagram Any ideas?