A
21.6-g copper ring has
a diameter of 2.54000 cm at
its temperature of
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Solution: Click For PDF Version In solving this problem we will use two concepts: (i) thermal linear expansion, and (ii) conservation of heat energy.
It is given
that the temperature of the copper ring is
It is given
that the temperature of the aluminium sphere is
Let the
equilibrium temperature of the ring-sphere system after the two have
been in thermal contact be
The
linear thermal expansion coefficient of copper is
and the linear thermal expansion coefficient of aluminium is
Using the property of linear expansion we first determine the diameter of the ring and that of the aluminium sphere at the equilibrium temperature.
and
As the sphere
just passes through the ring at
or
It is a linear algebraic equation for T. We find
For we determining the mass of the aluminium sphere we will use the conservation of heat energy. The specific heat capacity of copper is
and that of aluminium is
The mass of
the copper ring is
Let the mass
of the aluminium sphere be
Change of heat energy of the aluminium sphere will be
Change of heat energy of the copper ring will be
From the conservation of energy, we have the condition
or
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.
An aluminium sphere has a diameter of 2.54533
cm at its temperature of
The sphere is placed
on top of the ring, and the two are allowed to come to thermal
equilibrium, no heat being lost to the surroundings. The sphere just
passes through the ring at the equilibrium temperature. We have to
find the mass of the sphere.
and its diameter is
.
