Question

Thermodynamics one

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(i) Define pure substance and comprehensively describe the phase changes of a pure substance considering water as an example. Use diagrams to illustrate your understanding of this point.. (1 mark) (ii) The variations of properties during phase-change processes are best studied and understood with the help of property diagrams including the T-v, P-v, and P-T diagrams for pure substances. Taking water as an example, comprehensively sketch and discuss how these tables (1 mark) (iii) Piston-cylinder device initially contains (50+n/100) L of liquid water at 40°C and 200 kPa. Heat is transferred to the water at constant pressure until the entire liquid is vaporized. (a) What is the mass of the water? (b) What is the final temperature? (c) Determine the total enthalpy change. (d) Show the process on a T-v, P-v diagram with respect to saturation lines (2 mark) (iv) 1-kg of carbon dioxide is compressed from 1 MPa and 200°C to 3 MPa in a piston-cylinder device arranged to execute a polytropic process for which PV1.25 constant. Determine the final temperature treating the carbon dioxide as a) an ideal gas and b) a van der Waals gas (equation can be taken from text book) (1 mark)

Answer 1

Pure substances are defined as substances that are made of only one type of atom or only one type of molecule (a group of atoms bonded together). The measure of whether a substance is pure is known as purity. For example, pure iron would only contain iron atoms, and, as in the sugar cube mentioned above, pure sugar would only contain molecules of the substance called sucrose.

The Basic Phase Diagram

pressure с solid liquid 22 3 vapour temperature

Phase Transitions

Moving from solid to liquid by changing the temperature

Suppose you had a solid and increased the temperature while keeping the pressure constant - as shown in the next diagram. As the temperature increases to the point where it crosses the line, the solid will turn to liquid. In other words, it melts.

pressure с solid liquid increase temperature at constant pressure T vapour temperature Solid melts at this temperature,

If you repeated this at a higher fixed pressure, the melting temperature would be higher because the line between the solid and liquid areas slopes slightly forward.

pressure с increase temperature at a higher pressure solid liquid original pressure T vapour temperature Original melting temperature Solid now melts at a higher temperature

So what actually is this line separating the solid and liquid areas of the diagram?

It simply shows the effect of pressure on melting point. Anywhere on this line, there is an equilibrium between solid and liquid. You can apply Le Chatelier's Principle to this equilibrium just as if it was a chemical equilibrium. If you increase the pressure, the equilibrium will move in such a way as to counter the change you have just made.

solid liquid For most substances, the solid occupies a smaller volume than the liquid.

If it converted from liquid to solid, the pressure would tend to decrease again because the solid takes up slightly less space for most substances. That means that increasing the pressure on the equilibrium mixture of solid and liquid at its original melting point will convert the mixture back into the solid again. In other words, it will no longer melt at this temperature.

To make it melt at this higher pressure, you will have to increase the temperature a bit. Raising the pressure raises the melting point of most solids. That's why the melting point line slopes forward for most substances.

Moving from solid to liquid by changing the pressure

You can also play around with this by looking at what happens if you decrease the pressure on a solid at constant temperature.

pressure Solid melts when the pressure drops to this value. с decrease pressure at a constant temperature solid liquid T vapour temperature

Moving from liquid to vapor

In the same sort of way, you can do this either by changing the temperature or the pressure.

pressure с increase temperature at constant pressure solid liquid decrease pressure at a constant temperature T vapour temperature

The liquid will change to a vapor - it boils - when it crosses the boundary line between the two areas. If it is temperature that you are varying, you can easily read off the boiling temperature from the phase diagram. In the diagram above, it is the temperature where the red arrow crosses the boundary line.

So, again, what is the significance of this line separating the two areas? Anywhere along this line, there will be an equilibrium between the liquid and the vapor. The line is most easily seen as the effect of pressure on the boiling point of the liquid. As the pressure increases, so the boiling point increases.

The critical point

You will have noticed that this liquid-vapor equilibrium curve has a top limit (labeled as C in the phase diagram), which is known as the critical point. The temperature and pressure corresponding to this are known as the critical temperature and critical pressure. If you increase the pressure on a gas (vapor) at a temperature lower than the critical temperature, you will eventually cross the liquid-vapor equilibrium line and the vapor will condense to give a liquid.

pressure c the aitical point increase pressure at a constant temperature solid liquid T vapour the aitical temperature temperature

This works fine as long as the gas is below the critical temperature. What, though, if your temperature was above the critical temperature? There wouldn't be any line to cross! That is because, above the critical temperature, it is impossible to condense a gas into a liquid just by increasing the pressure. All you get is a highly compressed gas. The particles have too much energy for the intermolecular attractions to hold them together as a liquid. The critical temperature obviously varies from substance to substance and depends on the strength of the attractions between the particles. The stronger the intermolecular attractions, the higher the critical temperature.

Moving from solid to vapor

There's just one more line to look at on the phase diagram. This is the line in the bottom left-hand corner between the solid and vapor areas. That line represents solid-vapor equilibrium. If the conditions of temperature and pressure fell exactly on that line, there would be solid and vapor in equilibrium with each other - the solid would be subliming. (Sublimation is the change directly from solid to vapor or vice versa without going through the liquid phase.)

Once again, you can cross that line by either increasing the temperature of the solid, or decreasing the pressure. The diagram shows the effect of increasing the temperature of a solid at a (probably very low) constant pressure. The pressure obviously has to be low enough that a liquid can't form - in other words, it has to happen below the point labelled as T.

pressure с solid liquid T vapour temperature increase temperature at a constant pressure

You could read the sublimation temperature off the diagram. It will be the temperature at which the line is crossed.

The Triple Point

Point T on the diagram is called the triple point. If you think about the three lines which meet at that point, they represent conditions of:

• solid-liquid equilibrium
• liquid-vapor equilibrium
• solid-vapor equilibrium

Where all three lines meet, you must have a unique combination of temperature and pressure where all three phases are in equilibrium together. That's why it is called a triple point.

If you controlled the conditions of temperature and pressure in order to land on this point, you would see an equilibrium which involved the solid melting and subliming, and the liquid in contact with it boiling to produce a vapor - and all the reverse changes happening as well. If you held the temperature and pressure at those values, and kept the system closed so that nothing escaped, that's how it would stay.

Normal melting and boiling points

The normal melting and boiling points are those when the pressure is 1 atmosphere. These can be found from the phase diagram by drawing a line across at 1 atmosphere pressure.

pressure с solid liquid 1 atmosphere T vapour normal M.Pt normal B.Pt temperature

Phase Diagram for Water

There is only one difference between this and the phase diagram that we've looked at up to now. The solid-liquid equilibrium line (the melting point line) slopes backwards rather than forwards.

In the case of water, the melting point gets lower at higher pressures. Why?

ice water Ice is less dense than water ... . so when it melts, the water formed occupies a smaller volume.

If you have this equilibrium and increase the pressure on it, according to Le Chatelier's Principle the equilibrium will move to reduce the pressure again. That means that it will move to the side with the smaller volume. Liquid water is produced. To make the liquid water freeze again at this higher pressure, you will have to reduce the temperature. Higher pressures mean lower melting (freezing) points.

Now lets put some numbers on the diagram to show the exact positions of the critical point and triple point for water.

pressure 218 atm с solid liquid 1 atm (101325 Pa) 0.006 atm (611 Pa) vapour M.Pt: 0°C B.Pt: 100°C 0.0098°C 374°C temperature

Notice that the triple point for water occurs at a very low pressure. Notice also that the critical temperature is 374°C. It would be impossible to convert water from a gas to a liquid by compressing it above this temperature. The normal melting and boiling points of water are found in exactly the same way as we have already discussed - by seeing where the 1 atmosphere pressure line crosses the solid-liquid and then the liquid-vapor equilibrium lines.

Just one final example of using this diagram. Imagine lowering the pressure on liquid water along the line in the diagram below.

The phase diagram shows that the water would first freeze to form ice as it crossed into the solid area. When the pressure fell low enough, the ice would then sublime to give water vapor. In other words, the change is from liquid to solid to vapor.

(ii)

T-v diagram for water 400 Critical Point Quality: x = V-VE Vfg m 300 Saturated Liquid Line Superheat Region Saturated Vapor Line 200 Temperature (deg C) Quality Region V - Vf Vfg = Vg - Vf 100 plot by izzi Vf 0.001 0 0.01 Vg 0.1 Specific Volume (m3/kg) 1 10

p-v diaram of water

P Per 22 MPa critical point TCR 16.5MPa 350°C 374°C Superheat Region Pressure 1 [email protected] 3.2MPa Quality Region 25'c 3.2kPa specific volume V?

p-t diagram of water