MECH221 Assignment mid #7 –Concordia University
9.11 Is it possible to have a copper–silver alloy that, at equilibrium, consists of a β phase of composition 92 wt%
Ag–8 wt% Cu and also a liquid phase of composition 76 wt% Ag–24 wt% Cu? If so, what will be the approximate
temperature of the alloy? If this is not possible, explain why.
Solution
It is possible to have a Cu-Ag alloy, which at equilibrium consists of a phase of composition 92 wt% Ag-
8 wt% Cu and a liquid phase of composition 77 wt% Ag-23 wt% Cu. From Figure 9.7 a horizontal tie line can be
constructed across the + L phase region at about 800 C which intersects the L–( + L) phase boundary at 76 wt%
Ag, and also the ( + L)– phase boundary at 92 wt% Ag.
9.13 A lead–tin alloy of composition 30 wt% Sn–70 wt% Pb is slowly heated from a temperature of 150°C (300°F).
(a) At what temperature does the first liquid phase form?
(b) What is the composition of this liquid phase?
(c) At what temperature does complete melting of the alloy occur?
(d) What is the composition of the last solid remaining prior to complete melting?
Solution
Upon heating a lead-tin alloy of composition 30 wt% Sn-70 wt% Pb from 150 C and utilizing Figure 10.8
as shown below:
Page 1 of 18
, (a) The first liquid forms at the temperature at which a vertical line at this composition intersects
the eutectic isotherm--i.e., at 183 C.
Page 2 of 18
, (b) The composition of this liquid phase corresponds to the intersection with the ( + L)–L phase
boundary, of a tie line constructed across the + L phase region just above this eutectic isotherm--i.e., CL = 61.9
wt% Sn.
(c) Complete melting of the alloy occurs at the intersection of this same vertical line at 30 wt% Sn with
the ( + L)–L phase boundary--i.e., at about 260 C.
(d) The composition of the last solid remaining prior to complete melting corresponds to the intersection
with –( + L) phase boundary, of the tie line constructed across the + L phase region at 260 C--i.e., C is about
13 wt% Sn.
9.16 For an alloy of composition 52 wt% Zn–48 wt% Cu, cite the phases present and their mass fractions at the
following temperatures: 1000°C, 800°C, 500°C, and 300°C.
Solution
This problem asks us to determine the phases present and their concentrations at several temperatures,
as an alloy of composition 52 wt% Zn-48 wt% Cu is cooled. From Figure 9.19 (the Cu-Zn phase diagram), which is
shown below with a vertical line constructed at the specified composition:
At 1000 C, a liquid phase is present; WL = 1.0
At 800 C, the phase is present, and W = 1.0
At 500 C, and phases are present, and from the tie lie constructed on the above diagram
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9.11 Is it possible to have a copper–silver alloy that, at equilibrium, consists of a β phase of composition 92 wt%
Ag–8 wt% Cu and also a liquid phase of composition 76 wt% Ag–24 wt% Cu? If so, what will be the approximate
temperature of the alloy? If this is not possible, explain why.
Solution
It is possible to have a Cu-Ag alloy, which at equilibrium consists of a phase of composition 92 wt% Ag-
8 wt% Cu and a liquid phase of composition 77 wt% Ag-23 wt% Cu. From Figure 9.7 a horizontal tie line can be
constructed across the + L phase region at about 800 C which intersects the L–( + L) phase boundary at 76 wt%
Ag, and also the ( + L)– phase boundary at 92 wt% Ag.
9.13 A lead–tin alloy of composition 30 wt% Sn–70 wt% Pb is slowly heated from a temperature of 150°C (300°F).
(a) At what temperature does the first liquid phase form?
(b) What is the composition of this liquid phase?
(c) At what temperature does complete melting of the alloy occur?
(d) What is the composition of the last solid remaining prior to complete melting?
Solution
Upon heating a lead-tin alloy of composition 30 wt% Sn-70 wt% Pb from 150 C and utilizing Figure 10.8
as shown below:
Page 1 of 18
, (a) The first liquid forms at the temperature at which a vertical line at this composition intersects
the eutectic isotherm--i.e., at 183 C.
Page 2 of 18
, (b) The composition of this liquid phase corresponds to the intersection with the ( + L)–L phase
boundary, of a tie line constructed across the + L phase region just above this eutectic isotherm--i.e., CL = 61.9
wt% Sn.
(c) Complete melting of the alloy occurs at the intersection of this same vertical line at 30 wt% Sn with
the ( + L)–L phase boundary--i.e., at about 260 C.
(d) The composition of the last solid remaining prior to complete melting corresponds to the intersection
with –( + L) phase boundary, of the tie line constructed across the + L phase region at 260 C--i.e., C is about
13 wt% Sn.
9.16 For an alloy of composition 52 wt% Zn–48 wt% Cu, cite the phases present and their mass fractions at the
following temperatures: 1000°C, 800°C, 500°C, and 300°C.
Solution
This problem asks us to determine the phases present and their concentrations at several temperatures,
as an alloy of composition 52 wt% Zn-48 wt% Cu is cooled. From Figure 9.19 (the Cu-Zn phase diagram), which is
shown below with a vertical line constructed at the specified composition:
At 1000 C, a liquid phase is present; WL = 1.0
At 800 C, the phase is present, and W = 1.0
At 500 C, and phases are present, and from the tie lie constructed on the above diagram
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