For alloys of two hypothetical metals A and B, there exist an ?, A-rich phase and a ?, B-rich phase.

From the mass fractions of both phases for two different alloys (given below), which are at the same temperature, determine the composition of the phase boundary (or solubility limit) for the following:

alloy composition fraction \alpha phase fraction \beta phase
60 wt% A - 40 wt% b 0.59 0.41
30 wt% A - 70 wt% b 0.14 0.86

46 and 20.67% wt A

Explanation:

Using.

W = (Cb - C)/(Cb - Ca)

Where

0.59 = (Cb - 60/(Cb - Ca) -- (1)

0.14 = (Cb - 30)/(Cb - Ca) (2)

From (1)

(Cb - Ca)0.59 = Cb - 60

0.59Cb - 0.59Ca = Cb - 60

1.59Cb = 60 - 0.59Ca

From (2)

(Cb - Ca)0.14 = Cb - 30

0.14Cb - 0.14Ca = Cb - 30

1.14Cb = 30 - 0.14Ca

Cb = (30 - 0.14Ca)/1.14

Substitute (30 - 0.14Ca)/1.14 for Cb

1.59(30 - 0.14Ca)/1.14 = 60 - 0.59Ca

47.7 - 0.2226Ca = 1.14 * 60 - 1.14 * 0.59Ca

47.7 - 0.2226Ca = 68.4 - 0.6726Ca

47.7 - 68.4 =- 0.6726Ca + 0.2226Ca

-0.45Ca = -20.7

Ca = -20.7/-0.45

Ca = 46

Cb = (30 - 0.14Ca)/1.14

Cb = 30 - 0.14 * 46)/1.14

Cb = 20.67

answer:

c

explanation: