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Articles: Devotion | In quest of infinity - 9
- Prof. venkata ramanamurty mallajosyula
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QUESTION 2: How does a curve of type (a) switch over to a curve of type (b) when temperature is lowered below the freezing point? That is left as a puzzle!
We have two curves here. Let us start with curve (a). It represents the energy curve for the liquid. The x-axis specifies the “state” of the system. The point x = 0 corresponds to the ideal liquid state; and this also happens to be the state of lowest energy. Hence, if the temperature is right [and for water, any temperature above 0 degrees Celsius is favourable for existence as a liquid], the state of minimum energy is clearly the liquid state. When we consider a temperature below the freezing point [equal to 0 degrees Celsius in the case of water], the curve changes to the shape indicated in (b).
Notice that that the energy is zero not corresponding to the state that applied above 0°C but at a different point [representing a different state]. Till zero degrees Celsius is reached, the preferred state is liquid, but when the temperature is lowered below zero Celsius, something happens. That is because the system always seeks the state of lowest energy. Below 0°C, that state of minimum energy is not a liquid but something else [that of ice]. That is how freezing occurs.
Physicists do not use vague words like ‘state’ and so forth. They instead use the word order parameter. In the example considered here, for the liquid state, the order parameter has a value equal to zero while for the crystalline state, the order parameter is non-zero. The connection between symmetry, symmetry breaking and order parameter is very important and maybe I should digress a bit to explain what it is all about. This is best done by considering a magnetic substance like iron.
Iron is made up of iron atoms and the interesting point is that every atom is like a tiny magnet. Imagine the magnetic atom to be like an arrow, pointing in a certain direction. If you take a lump of iron, the question now is in which direction will the different arrows point? That depends on the temperature of the lump. If it is above 770°C, then the arrows would all point randomly; if, however, the temperature is below 770°C, then the arrows all point in the same direction, as illustrated below.
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