Monday, February 6, 2012

Real and apparent expansion of a liquid &Density calculation related to coefficient of expansion

expansion of various liquids

Expansion of  liquids

        The expansion of a liquid may be shown by means of a flask fitted with a rubber bung and a length of glass tubing ( as shown in the picture above). The flask is filled with water or other liquid and the bung pushed in until the level of the liquid comes a short distance up the tube.
Variation of water volume with temperature & Compensated dilatometer

        On plunging the flask into a can of hot water it is noticed that the level of the liquid at first falls slightly and then starts to rise steadily.

       The initial fall in level is caused by the expansion of the glass which becomes heated and expands before the heat has had time to be conducted through the glass into the liquid.

To compare the expansion of various liquids

      Different liquids have different thermal expansions. To demonstrate this, several fairly large glass bulbs with glass stems are filled to a short distance above the bulb with various liquids ( as shown in the picture above.).

       In order to make a fair comparison, the bulbs and stems must all be of the same size. The bulbs are immersed in a metal through containing cold water and left until they have reached a steady temperature. A little extra liquid should now be added, where necessary, to make all levels the same.

     The bath is now heated and well stirred to ensure a uniform temperature. When the bulbs and their contents have acquired the new temperature of the bath it will be seen that the liquid levels have risen by different amounts.

Thus, for a given rise in temperature, equal volumes of different liquids show different expansions in volume.

The coefficient of real and apparent expansion of a liquid

     Unlike solids, liquid have no fixed length or surface area but always take up the shape of the containing vessel. Therefore, in the case of liquids we are concerned only with volume changes when they are heated.

The coefficient of real ( or absolute ) expansion of a liquid is the fraction of its volume by which it expands per degree rise in temperature.

Any attempt at direct measurement of the expansion of a liquid is complicated by the fact that the containing vessel itself expands.

However, since liquids must always be kept in some kind of vessel, it is just as useful to know the apparent expansion of a liquid, which is the difference between its real expansion and the expansion of the vessel.

   The coefficient of apparent expansion of a liquid is the fraction of its volume by which the liquid appears to expand per degree rise in temperature when heated in an expansible vessel.

Density calculation related to coefficient of expansion

     When a fixed mass of substance expands, the increase in volume will bring about a decrease in density. This principle applies to all substances, but has a special application to liquids.

Liquids have no fixed length or surface area but take up the shape of their containing vessel. In such cases we are concerned only with the coefficient of cubical expansion.

Now, with the equations.

     Suppose we take a mass, m, of a substance whose coefficient of cubical expansion is γ. If the initial volume is V1, and the temperature is raised by θ, then the new volume V2 is given by,

V2 = V1( 1 + θ γ)

Now, mass = density × volume

hence, if the initial and final densities are ρ1 and ρ2 respectively, then since the mass remains constant- in classical mechanics- ,

m = ρ1 V1 = ρ2 V2

ρ1/ρ2 = V2/V1 = V1( 1 + θ γ) / V1 = 1 + θ γ

This relationship is used to measure the coefficient of cubical expansion of a liquid in terms of its density at two different temperatures.

Coming up : The unusual expansion of water ( that you see in the picture above) and biological importance of the anomalous expansion of water. I hope that was useful. Thanks for visiting:)

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