Saturday, February 4, 2012

The coefficient of linear expansion: definition and applications

To define the coefficient of linear expansion

    We have seen that various substances do not expand equally when their temperatures are raised ( see useful Applications of thermal expansion). Their properties in this respect are expressed by the coefficient of linear expansion, which is defined as follows.

The coefficient of linear expansion of a substance is the fraction of its original length by which a rod of the substance expands per degree rise in temperature.

Let's see an example:

The original length of brass rod =50.2 cm

Initial temperature of rod = 16.6 C

Final temperature of rod = 99.5 C

1st micrometer reading = 4.27 mm

2nd micrometer reading = 3.48 mm

Rise in temperature of rod = 99.5 - 16.6 = 82.9 C

Expansion of rod = 4.17 -3.48 =0.79 mm = 0.079 cm

Coefficient of linear expansion= expansion / original length × rise in temperature

Coefficient of linear expansion=0.079 / 50.2 × 82.9 = 0.000019 / C.

Compensation for expansion in clocks and watches

    When pendulum clocks first came into general use in the eighteenth century it was found that they lost time during warm weather owing to expansion of the pendulum.

Various methods were therefore devised to compensate for this, and two of historic interest are shown in Fig.


John Harrison's- pendulum

The mercurial pendulum

     The mercurial pendulum invented by George Graham consists of a cylindrical glass vessel of mercury supported by an iron rod. The depth of mercury is adjusted so that the downward expansion of the rod is exactly compensated by the upward expansion of the mercury.

John Harrison's "gridiron" pendulum depends on the differential expansion of a set of brass and iron rods.
Now the coefficients of expansion of brass and iron are approximately in the ratio of 3 to 2.

In the gridiron pendulum it is arranged that three lengths of iron expand so as to lower the bob, while two lengths of brass expand so as to raise it.

The net result is that the position of the bob remains unaltered as the temperature changes.

Watches are controlled by a balance, which is a small wheel with a heavy rim, oscillating to and fro under the action of a hairspring.

An increase in temperature causes the
watch to lose time for two reasons. It increases the diameter of the wheel and weakens the elasticity of the hairspring.

Compensation is effected by making the rim of the wheel of bimetallic strip and dividing it into two portions as shown in Fig. A rise in temperature causes the strip to bend inwards, which compensates both for the outward expansion of the spokes and the reduced elasticity of the hairspring. You see that I like old watches:)

Thermal expansion in the kitchen

Pyrosil in the kitchen

       Most people know that hot water should never be poured into thick glass tumblers or dishes, since they are liable to crack. Glass is a poor conductor of heat, so that when hot liquid is poured into the glass the inside becomes hot while the outside remains cold. Expansion of the inside thus sets up a strain which cracks the glass.

     Very often, cold jam-jars will crack when hot jam is poured into them. However, this may be prevented if the jars are first heated slowly in a warm oven before filling them.
Special glassware and ceramics of low coefficient of expansion are obtainable for kitchen and laboratory use. Pyrex and Pyrosil are examples. Even when very hot, dishes or breaks made of these materials may be plunged into cold water without cracking.

 How to remove a tight glass stopper
 Glass stopper in bottles often become tightly fixed, and attempts to remove them by force generally result in breaking. The following treatment is invariably successful.

   Two pairs of hands are required. One person holds the bottle firmly on the table, while another rapidly pulls to and fro a strip of cloth which has been wrapped once round the neck of the bottle. Work done against friction between cloth and glass becomes converted into internal energy in the glass. This raises the temperature and causes the neck to expand sufficiently for the stopper to be withdrawn easily.
  I hope it works with you :)