Question

2 parts thx!

1. A flat aluminum plate has a circular hole of diameter 1.739
cm at 0.00 °C.What is the change in its diameter when the
temperature of the plate is increased to 116 °C? For reference, the
coefficient of thermal expansion for aluminum is 2.3 x
10^{-5}/C°. Give at least 2 significant figures in your
answer, which should be in cm.

2. A flat plate made of an unknown metal has a circular hole of
diameter 2.89 cm at 0.00 °C that increases in diameter by 0.004
when the temperature is raised from 0.00 °C to 113 °C. What is the
coefficient of thermal expansion for this unknown
metal. Express your answer in parts per million per
degree Celsius (for example, an expansion coefficient of 23 x
10^{-6}/°C would be 23 ppm/°C). However, enter only the
numerical part of the answer.

Answer #1

A hole in an Aluminum plate has diameter of 1.235 cm at 200C
[???= 25 × 10−6?0−1, ???= 75 × 10−6?0−1]
i. What is the diameter of the hole at 2000C?
ii. At what temperature is the diameter of the hole equal to 1.176
cm?

At 20∘C, the hole in an aluminum ring is 2.200 cm in diameter.
You need to slip this ring over a steel shaft that has a
room-temperature diameter of 2.204 cm .
To what common temperature should the ring and the shaft be
heated so that the ring will just fit onto the shaft? Coefficients
of linear thermal expansion of steel and aluminum are
12×10-6K-1 and
23×10-6K-1 respectively.
Express your answer in degrees Celsius to two significant
figures.

At 20∘C, the hole in an aluminum ring is 2.100 cm in diameter.
You need to slip this ring over a steel shaft that has a
room-temperature diameter of 2.107 cm To what common temperature
should the ring and the shaft be heated so that the ring will just
fit onto the shaft? Coefficients of linear thermal expansion of
steel and aluminum are 12×10−6 K−1 and 23×10−6 K−1
respectively.

A cylindrical pin of diameter 20 cm, made of aluminum, does not
fit through a 19.97cm circular hole in a copper plate. The pin and
the copper plate both are initially at a temperature of 110 degrees
C. At what temperature, in degrees C, does the cylindrical pin just
fit into the circular hole of the copper plate if both the plate
and the pin are cooled together?

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