**Problem and solution**

In a iron disc there is a hole at the center. A brass rod of
equal size is exactly fixed in the hole. To get the brass rod out of the hole,
what shall we do with respect to temperature?

To solve this problem we shall understand one simple concept.
Coefficient of linear expansion is a measure of expansion of the material with
respect to the rise of the temperature. It is also a measure of contraction of
a material with respect to the decrease in temperature.

If a material is having a higher value of coefficient of
linear expansion, with the increase of the temperature at expands more and with
the decrease of the temperature it contracts more.

We know that coefficient of linear expansion of brass is more
than that of iron. Hence if you rise the temperature brass expands more and it
becomes further very tight in the hole.

If you decrease the temperature brass contracts more
therefore it can be taken out from the hole quite easily.

**Problem and solution**

Two different materials are having different lengths at a
certain temperature. What is the condition for the difference between the two
material lengths always remains constant at all temperatures?

If the difference between the two lengths has to remain
constant, both of them shall increase their lengths by the same value with
respect to the increase in the temperature. So we shall equate the increase in
the lengths of both of them.

**Problem and solution**

Find the ratio of expansions in the two wires when same heat
energy is supplied to both of them?

When same temperature is given to both of them we can say
that the increase in the length of the materials is directly proportional to
its length, coefficient of linear expansion and the rise in the temperature.

When the same heat energy is given to both of them they are
not going to expand equally. The material with more specific heat will expand
less and vice versa. So we shall take the concept of specific heat into
consideration while solving this problem. It can be proved that the increase in
the length in this case is going to be independent of the length of the
material but depends on the area of its cross-section.

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