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

composition of alpha phase is 27% B

Step-by-step 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

`(C_\beta - Co)/(C_\beta - Ca)` = 0.5

`(87 - 57)/(87 - Ca)` = 0.5

solve it we get

Ca = 27

so composition of alpha phase is 27% B