Question

A hypothetical A-B alloy of composition 57 wt% B-43 wt% A at some temperature is found to consist of mass fractions of 0.5 for both and phases. If the composition of the phase is 87 wt% B-13 wt% A, what is the composition of the phase

Answer 1

Answer:

composition of alpha phase is 27% B

Explanation:

given data

mass fractions  = 0.5 for both

composition = 57 wt% B-43 wt% A

composition = 87 wt% B-13 wt% A

solution

as by total composition Co = 57 and by beta phase composition  Cβ = 87  

we use here lever rule that is

Wα = Wβ   ...............1

Wα = Wβ = 0.5

now we take here left side of equation

we will get

$\frac{C_\beta - Co}{C_\beta - Ca}$   = 0.5

$\frac{87 - 57}{87 - Ca}$ = 0.5  

solve it we get

Ca = 27

so composition of alpha phase is 27% B