Respuesta :
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
[tex]\frac{C_\beta - Co}{C_\beta - Ca}[/tex] = 0.5
[tex]\frac{87 - 57}{87 - Ca}[/tex] = 0.5
solve it we get
Ca = 27
so composition of alpha phase is 27% B
The composition of the phase is; 27
What is the composition of the alloy?
Mass fractions for both; w_a = w_b = 0.5 for both
Composition of A-B alloy; C_o = 57 wt% B - 43 wt% A
New composition of the phase; C_b = 87 wt% B - 13 wt% A
Using the Lever rule that is used to determine the mole fraction (x_i) or the mass fraction (w_i) of each phase of a binary equilibrium phase, we have;
W_a = W_b = 0.5
This gives us;
(C_b - C_o)/(C_b - C_a) = 0.5
(87 - 57)/(87 - C_a) = 0.5
30/0.5 = 87 - C_a
60 = 87 - C_a
C_a = 87 - 60
C_a = 27
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