In the previous section we saw change of phase. In this section we will see phase diagram and triple point
First let us see the relation between pressure and temperature. It can be written in 7 steps:
1. We have seen that, when external pressure on the surface of a liquid is increased, it becomes difficult for that liquid to boil
• That means, when the external pressure is increased, it becomes difficult to change from liquid state to gaseous state
• We can say that, external pressure tries to prevent the liquid from changing into a gas
2. We know that: Liquid is denser than gas
• So we can say that, external pressure tries to compress the body into a denser state
• If pressure is increased further, the liquid will even become a solid
3. But besides pressure, we have to consider another factor also. It is: temperature
• Temperature acts in the opposite sense
• When temperature is increased, it becomes difficult for a liquid to stay in the liquid state. It will be forced to change into gaseous state
• Similarly, when temperature is increased, it becomes difficult for a solid to stay in the solid state. It will be forced to change into liquid state
4. So we can write two points:
(i) When pressure increases, an increase in density occurs in the direction:
Gas → Liquid → Solid
(ii) When temperature increases, a decrease in density occurs in the direction:
Solid → Liquid → Gas
5. The reverse can also be written:
(i) When pressure decreases, a decrease in density occurs in the direction:
Solid → Liquid → Gas
(ii) When temperature decreases, an increase in density occurs in the direction:
Gas → Liquid → Solid
♦ For example, we obtain solid ice by decreasing the temperature of liquid water
6. We get an interesting result from 4(i) and 5(ii):
• If we can obtain sufficiently high pressure, and sufficiently low temperature, we can change gases into solids.
♦ For example, scientists have succeeded in making solid hydrogen in the lab
✰ Note that, the end result in both 4(i) and 5(ii) is 'solid'
7. So pressure and temperature has a somewhat inverse relation with each other:
♦ High pressure and low temperature gives solid state
♦ Low pressure and high temperature gives gaseous state
♦ Intermediate values of pressure and temperature gives liquid state
• We can plot a graph with pressure along the y-axis and temperature along the x-axis
• Such a graph is known as P-T diagram or phase diagram
Before discussing about the P-T diagram, we have to first become familiar with the chart shown in fig.11.12 below:
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| Fig.11.12 |
• The chart shows that:
♦ A change from solid state to liquid state is called melting
♦ A change from liquid state to solid state is called freezing
♦ A change from liquid state to gaseous state is called vaporization
♦ So on . . .
• We will need to mention these terms when we discuss about P-T diagram
• Now we will see the details about P-T diagram
• Every substance has it’s own unique P-T diagram
• Scientists have already prepared them for various substances
♦ All we need now, is to learn the common features of those diagrams
♦ While we discuss those common features, we will learn how a P-T diagram is prepared
• The features can be written in 13 steps
1. Fig.11.13 below shows a P-T diagram
♦ Pressure is plotted along the y-axis
♦ Temperature is plotted along the x-axis
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| Fig.11.13 |
2. When the x and y axes are drawn, we get the x-y plane
♦ In our present case, x-y plane is the P-T plane
• In the fig.11.13 above, the P-T plane is divided into three regions: orange, blue and gray
3. In the P-T plane, there are infinite number of points
• Each of those points will be in the form: (T.P)
• Pick any one of those points from the plane. Let it be (Ti, Pi)
• We can write three properties:
(i) If the point is from the orange region:
♦ Apply a pressure of Pi on a sample of that substance
♦ Bring the temperature of that sample to Ti
♦ Then the sample will change into solid state
(ii) If the point is from the blue region:
♦ Apply a pressure of Pi on a sample of that substance
♦ Bring the temperature of that sample to Ti
♦ Then the sample will change into liquid state
(iii) If the point is from the gray region:
♦ Apply a pressure of Pi on a sample of that substance
♦ Bring the temperature of that sample to Ti
♦ Then the sample will change into gaseous state
4. Note that, the solid region (orange) is towards the left of the graph
♦ Here, temperatures will be low
♦ We know that, at low temperatures, substances tend to solidify
• In this way, we can characterize the blue and gray regions also
• Now we know the significance of the three regions in the P-T diagram
5. Next, we will see the three curves: red, yellow and green
♦ The yellow curve separates the solid and liquid regions
♦ The green curve separates the liquid and gaseous regions
♦ The red curve separates the solid and gaseous regions
6. Consider the yellow curve
We can write a description in 7 steps:
(i) There are infinite number of points on the yellow curve
• Take any one point from them. Let it be (Ti,Pi). It is marked with a ‘⨯’
♦ Apply a pressure of Pi on a sample of that substance
♦ Bring the temperature of that sample to Ti
(ii) Then we can write:
♦ If the sample is initially in the solid state, it will begin to melt
♦ If the sample is initially in the liquid state, it will begin to freeze
(iii) This is because, the yellow curve is the transition between solid and liquid
• Along this curve, the sample is partially solid and partially liquid
(iv) keeping temperature constant at Ti, let us increase the pressure
• This is indicated by the vertical double headed arrow
♦ The pressure moves upwards along that arrow
♦ Then the sample is no longer ‘melting/freezing’
♦ All the liquid portion will freeze
♦ Thus It will enter the orange region and become a complete solid
• This is what we would expect because, increasing pressure gives denser substances
(v) keeping temperature constant at Ti, let us decrease the pressure
♦ Now the pressure moves downwards along the vertical double headed arrow
♦ Then the sample is no longer ‘melting/freezing’
♦ All the solid portion will melt
♦ Thus it will enter the blue region and become a complete liquid
• This is what we would expect because, decreasing pressure gives less denser substances
(vi) keeping pressure constant at Pi, let us increase the temperature
• This is indicated by the horizontal double headed arrow
♦ The temperature moves towards the right along that arrow
♦ Then the sample is no longer ‘melting/freezing’
♦ All the solid portion will melt
♦ Thus It will enter the blue region and become a complete liquid
• This is what we would expect because, increasing temperature gives less denser substances
(vii) keeping temperature constant at Ti, let us increase the pressure
♦ Now the pressure moves towards the left along the double headed arrow
♦ Then the sample is no longer ‘melting/freezing’
♦ All the liquid portion will freeze
♦ Thus it will enter the orange region and become a complete solid
• This is what we would expect because, increasing pressure gives denser substances
7. So the yellow curve is a transition between solid and liquid
We can write similar steps for the green curve:
(i) Consider any convenient point on the green curve. Let it be (Ti,Pi). It is marked with a ‘⨯’
♦ Apply a pressure of Pi on a sample of that substance
♦ Bring the temperature of that sample to Ti
• A portion of the sample will be in the liquid state
• The remaining portion will be in the gaseous state
(ii) Keeping temperature constant, increase the pressure
♦ This is an upward motion along a vertical double headed arrow
♦ The vapor portion will condense and the sample will become a complete liquid
♦ The sample will enter the blue region
(iii) Keeping temperature constant, decrease the pressure
♦ This is a downward motion along the vertical double headed arrow
♦ The liquid portion will vaporize and the sample will become a complete vapor
♦ The sample will to enter the gray region
(iv) Keeping pressure constant, increase the temperature
♦ This is a rightward motion along a horizontal double headed arrow
♦ The liquid portion will vaporize and the sample will become a complete vapor
♦ The sample will enter the gray region
(v) Keeping pressure constant, decrease the temperature
♦ This is a leftward motion along the horizontal double headed arrow
♦ The vapor portion will condense and the sample will become a complete liquid
♦ The sample will enter the blue region
8. We can write similar steps for the red curve:
(i) Consider any convenient point on the red curve. Let it be (Ti,Pi). It is marked with a ‘⨯’
♦ Apply a pressure of Pi on a sample of that substance
♦ Bring the temperature of that sample to Ti
• A portion of the sample will be in the solid state
• The remaining portion will be in the gaseous state
(ii) Keeping temperature constant, increase the pressure
♦ This is an upward motion along a vertical double headed arrow
♦ The vapor portion will deposit and the sample will become a complete solid ♦ The sample will enter the orange region
(iii) Keeping temperature constant, decrease the pressure
♦ This is a downward motion along the vertical double headed arrow
♦ The solid portion will sublime and the sample will become a complete vapor
♦ The sample will to enter the gray region
(iv) Keeping pressure constant, increase the temperature
♦ This is a rightward motion along a horizontal double headed arrow
♦ The solid portion will sublime and the sample will become a complete vapor
♦ The sample will enter the gray region
(v) Keeping pressure constant, decrease the temperature
♦ This is a leftward motion along the horizontal double headed arrow
♦ The vapor portion will deposit and the sample will become a complete solid
♦ The sample will enter the orange region
9. So the significance of the three curves is now clear. It can be written in 3 steps:
(i) Along the yellow curve:
♦ A portion of the sample will be in the solid state
♦ The remaining portion will be in the liquid state
■ This curve is called fusion curve
(ii) Along the green curve:
♦ A portion of the sample will be in the liquid state
♦ The remaining portion will be in the gaseous state
■ This curve is called vaporization curve
(ii) Along the red curve:
♦ A portion of the sample will be in the solid state
♦ The remaining portion will be in the gaseous state
■ This curve is called sublimation curve
10. So, at the point of intersection of the three curves:
♦ A portion of the sample will be in the solid state
♦ Another portion of the sample will be in the liquid state
♦ The remaining portion will be in the gaseous state
■ This point of intersection of the three curves is called triple point
11. Imagine a horizontal line through the triple point
• Above that horizontal line, orange, blue and gray regions are present
• Below that horizontal line, only orange and gray regions are present
♦ There is no blue region
■ So it is clear that:
If the pressure of a sample is below the ‘pressure at triple point’, then that sample cannot be in the liquid state
12. Imagine a vertical line through the triple point
• To the right of that vertical line, orange, blue and gray regions are present
• To left of that vertical line, only orange and gray regions are present
♦ There is no blue region
■ So it is clear that:
If the temperature of a sample is below the ‘temperature at triple point’, then that sample cannot be in the liquid state
13. Another important point is the critical point
• This point is at upper portion and towards the right side of the graph
♦ Since it is at the upper portion, pressure will be very high
♦ Since it is towards the right side, temperature will also be very high
• But even if the pressure is very high, substances cannot exist as solid
♦ This is because of the very high temperature
• So at the critical point, portion of the sample will be in the liquid state
♦ The remaining portion will be in the gaseous state
• If the temperature or pressure is increased beyond the critical point, the liquid and gaseous portions will become indistinguishable from each other
• We will learn about the applications of critical point in higher classes
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