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Sunday, 29 July 2018

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Liquid expansion: Real and apparent expansion, cubic expansivity.




Expansion of liquid; Real and apparent expansivity

Like solid, liquid expands on heating and contracts on cooling, because liquid is always held in a container, the expansion of liquid is always complicated because of the expansion of the container itself.



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Real and apparent expansivity

Since the expansion of liquid is complicated because of the expansion of the container, it is therefore necessary to distinguish between the real and apparent cubic expansivity of liquid.

Real expansion = Apparent expansion + Expansion of the container


Real cubic expansivity

The real (or absolute) cubic expansivity of a liquid can be denoted by “ɣr”, it is the absolute increase in volume, per unit volume, per degree rise in temperature.


Apparent Cubic expansivity

The apparent cubic expansivity of a liquid can be denoted by “ɣa”, it is the increase is volume, per unit volume, per degree rise in temperature, when the liquid is heated in an expansible vessel.

The apparent cubic expansivity ɣa” depends also on the cubic expansivity ɣ”. Therefore, the real expansivity of liquid ɣr” is always more than the apparent expansivity of liquid ɣa”, it can be shown that the difference between the rel an apparent expansivity of a liquid is the cubic expansivity of the vessel.

Therefore,
ɣr = ɣa + ɣ


FORMULAR

ɣr = ɣa + ɣ

Apparent expansivity can be calculated given the mass liquid expelled over mass of the liquid remaining, multiplied by the temperature rise.

Let,
m = Mass
e = density
V = volume
ɣa = Apparent cubic expansivity
θ = Change in temperature
Therefore,
ɣa = (m1 -m2) / m2(θ1- θ2)


An Example 

A density bottle holds 250 of liquid at 30°C and only 248.5 at 60°C, find;
a) the apparent expansivity
b) the real expansivity
Given linear expansivity = 0.000006 per kelvin.

Solution
ɣa = (m1 -m2) / m2(θ1- θ2)
ɣa = (250 -248.5) / 248.5(60- 30)
ɣa = 0.000201207
Cubic expansivity = 3*Linear expansivity
ɣ = 3*(0.000006) = 0.000018 per kelvin
ɣr = ɣa + ɣ

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