An
aluminium cube 20 cm on
edge floats on mercury. We have to find how much farther will the
block sink when the temperature rises from
270 to 320 K. (The coefficient of volume
expansion of mercury is
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Solution: Click For PDF Version
In answering
this problem we will use the property of volume expansion of mercury
and determine its density at 270 K and at 320 K from its density at
293 K,
The coefficient of volume expansion is defined as
Therefore,
change in density with change
We thus find
And
We use for
the density of aluminium,
Therefore, the mass of aluminium cube of edge 20 cm is
The height, h, of the aluminium block inside the mercury at 270 K can be determined from the buoyancy principle. It will be
When the
aluminium block is placed in mercury at 320 K the area of its base
would have expanded because of thermal expansion. The coefficient of
thermal expansion of aluminium is
The area of the base of the aluminium block will be
Therefore,
the height,
Therefore, the additional height by which the aluminium block will sink inside mercury with the change in temperature from 270 K to 320 K will be
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.)
.
We expect that the aluminium block will sink further in mercury as
the temperature of mercury changes from 270 K to 320 K because of
the change in density.
in
temp will be
.
.
Therefore, the change in area of the base of the aluminium cube will
be
.
,
of the aluminium cube inside the mercury at 320 K can be determined
by using the density of mercury at 320 K. It will be
