We can now see what is happening when we heat a substance as it is changing phase. The energy is going into making the matter further apart; that is to say the atoms are less well bound when they are further apart. Because energy is being expended in the process the atoms are not just being separated, they are being forced up some kind of a hill. In physical terms the energy is going into potential energy which can be recovered later.
We are not so much looking at a hill but more at a valley between two hills, or perhaps more realistically, like the moat around a hill castle. Such a moat is called a potential well.
What is plotted here is the potential energy U
The bottom of the well corresponds to the minimum energy so one of the particles, if free to move, will go to this position with respect to the other particle. Any movement in either direction is uphill so the particle returns to its stable position. Under these circumstances the particles are "bound" and the "binding energy" is the depth of the well in energy units below the horizontal axis. The deeper the well the more firmly bound are the two particles. The separation of the two particles in this situation is thus
At non-zero temperatures (on the absolute Kelvin temperature scale) the particles will have some motion and therefore some kinetic energy. So the bound particle will not sit at the bottom of the well but a little way up, say at the level A-A. Since the particle can occupy any position along A-A it can have any separation within the limits defined by the two ends of the line A-A. This is as if the two particles were bound by a piece of elastic. Their mean separation is now
If we were to raise the kinetic of the particles by an amount equal to the depth of the well the particles become unbound and the bond broken. This is what happens when for example we heat molecular hydrogen and So we can see from this that energy is absorbed into potential energy when bonds are broken and the particles move further apart. Conversely potential energy is released as kinetic energy when the particles move closer together, bind and become more stable.
Yes. This follows from the discussions above since phase transitions are a manifestation of changes in the binding energy.
What is essential is to effect a change in the inter-atomic separation such that the atoms can then re-arrange themselves. It does not matter too much how that change is effected. A more obvious mechanism than a change in temperature is in fact a change in pressure. By changing the pressure the atoms can be caused to be closer or further apart. Temperature and pressure in this sense act in opposition. The separation of atoms is decreased by increasing the pressure but can then be restored by increasing the temperature. We can see this in the diagram below which characterises the transition between a gas and liquid.
What each curve tells us is what happens to the pressure as we change the volume containing the gas, keeping the temperature of the gas fixed. We can visualise this system as being the volume contained by a piston which we can move in and out, though in so doing we must allow the system always to return to its constant temperature (i.e. isothermal expansion/contraction). Consider the curve marked T So an increase in pressure brings about a change of state from the gas to the liquid. We can recover the situation by increasing the temperature, i.e. by moving diagonally from bottom left to upper right.
For temperatures greater than T
Yes, it is. We can see this from the diagram we have just been discussing.
As we move to higher and higher temperatures the curves appear to have less distortion and begin to indicate the characteristic reciprocal relationship between the two parameters pressure and volume, P 1/V or more simply PV=constant. This is the
Hence as the volume is decreased (a) is no longer a good assumption and so our effective volume has to be decreased by the amount occupied by the atoms/molecules. That is we should replace V by (V-b) where b is some small constant (volume). Also when the atoms are relatively close they experience the attractive force between them which we discussed earlier and which is equivalent to a sort of external pressure. Therefore P also has to be modified in a way which increases with volume decrease. Hence P can be replaced by
or, in its more general form
where R is the universal gas constant. This equation is known as van der Waals equation and describes the distortions in the graph above very accurately, that is it describes the behaviour of a gas close to its phase transition.
It follows from the discussion above that the conditions for a phase transition are defined by temperature and pressure. For a given temperature less than the critical temperature there is a pressure at which a transition occurs, and similarly at a given pressure there will be a temperature for transition. The respective values will also depend on the substance. Hence there are combinations of temperature and pressure associated with each state of matter delineated by boundaries, a transition of which results in a phase change. For example, the curve below shows these combinations for water. X marks the boiling point for water at normal pressure.
The critical temperature, T
We can see from this that for temperatures greater than T
Glasses are very viscous (stiff) fluids and essentially have the same structure as a liquid. The atoms are not in any regular structure but are orientated randomly. Given enough time glasses will flow. Plasmas are formed when atoms are ionised, that is when the electomagnetic bond between the negatively charged electron (or electrons) and the positively charged nucleus is broken and the electrons are separated from the ion it leaves behind. This ionisation energy is very similar to latent heat but the energies involved are very much greater. Calculate how much energy is required to ionise 1 kg of the water radical OH (which, to a first approximation, has the same atomic weight as a water molecule). The ionisation potential of OH is 13.0 eV. Click here for the answer. |
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