We were discussing “Triple point phase diagram of water and “PV diagram of pure substance” as well as we have also seen the concept of temperature entropy diagram of water “in our previous posts. Now it’s time to go ahead to discuss another topic in the category of thermal engineering.

Today we will see here the T-V diagram of a pure substance with the help of this post.

Let us first see here some basic introduction parts and then we will draw the T-V diagram of a pure substance. Water boils at a temperature of 1000C. Is it correct? No this is not correct answer because we have not mentioned the value of pressure here. We will have to say that water boils at a temperature of 1000C at a pressure of 1 atm.

Let us think that we have increased the value of pressure and now new pressure is 5 atm, in this situation boiling point of water will also be increased and it will have some value but will be greater than 1000C. So we will have two important terms here i.e. saturation temperature and second one is saturation pressure.

If we keep the pressure constant, temperature at which a pure substance will change its phase will be termed as saturation temperature. Similarly if we keep the temperature constant, pressure at which a pure substance will change its phase will be termed as saturation pressure.

### Let us come to the main subject i.e. T-V diagram of pure substance

Let us consider one cylinder piston arrangement as shown in figure. Let us consider that initially working fluid is water and it is contained inside the cylinder at a temperature of 200C. Let us consider that we are providing heat energy to the system at constant pressure.

As we are providing heat energy to the cylinder or to the system at constant pressure of 1 atm. Therefore temperature of water will increase and volume or specific volume of water will also increase slightly. Let we are providing heat energy to the system till water reaches to saturation temperature at 1 atm pressure i.e. 1000C. Hence we will have one process 1-2. During this process water is heated at constant pressure of 1 atm from 200C to 1000C. Finally water will be at saturated liquid state at point 2 as displayed in figure.
Let us think that we are providing more heat energy to the system. Now temperature will be constant and boiling of water will be started. At state 3, as displayed in figure, we will have liquid vapour mixture. Finally working fluid will reach to point 4, by heating at constant temperature and constant pressure, where there will not be a single drop of liquid in working fluid and this point will be termed as saturated vapour state.

Let us think that we are providing more heat energy to the system. Saturated vapour will now be converted in to super heated steam and during this process temperature will be increased. Super heated steam is displayed in figure by a point 5 in above figure.

So we have one curve, between temperature versus volume for a pure substance (water in this example), and we have displayed this curve by the process 1-2-3-4-5.

So we have drawn the T-V curve for displaying the phase change process of water at a pressure of 1 atm. Now in order to secure the T-V diagram of pure substance, we will have to draw the similar curve for other pressure values also.

Let we have added weights over the piston in order to increase the pressure value of the system. Let now system is at pressure of 1 MPa. Now we will see some important points.
T-V diagram for pure substance

Working fluid i.e. water is now at pressure of 1 MPa, let us consider that we are providing the heat energy to the system at constant pressure of 1 MPa. We will again secure one another T-V curve as shown in figure for pressure of P2, we have taken P2 for the value of pressure 1 MPa . T-V curve for both pressure values will be quite similar to each other but there will be some differences and we will see these differences below.

Boiling point of water will be higher now as compared to that of earlier condition because operating pressure P2 (1 MPa) is higher in second case as compared to earlier operating pressure of P1(1 atm).

Specific volume or simply volume of saturated liquid at 1 MPa will be larger as compared to respective value for 1 atm pressure. Similarly, Specific volume or simply volume of saturated vapour at 1 MPa will be smaller as compared to respective value for 1 atm pressure.

Constant temperature line displayed by horizontal line in figure, which connects saturated liquid and saturated vapour states, will also be smaller as compared to that for 1 atm pressure.

Similarly if we draw the T-V curve for other higher pressure values, we will have similar other saturation lines or T-V curve but saturation lines will become shorter as we will go for increasing pressure.
Now we will combine each saturated liquid state point and we will have one line which will be termed as saturated liquid line. Similarly, we will combine each saturated vapour state point and we will have one line which will be termed as saturated vapour line. These two lines i.e. saturated liquid line and saturated vapour line meet with each other at a point which will be termed as critical point.

Therefore we can say that critical point will be defined as a point where saturated liquid state and saturated vapour state are identical.

Once we have joined the saturation liquid line and saturated vapour line, we will have one dome type of shape and that is T-V diagram for a pure substance.

Region left side of the saturated liquid line will be termed as compressed liquid region and similarly region right side of the saturated vapour line will be termed as vapour region and these two regions will be single phase region.

Region falls under the dome will be termed as saturated liquid-vapour mixture region or simply wet region.

Do you have any suggestions? Please write in comment box.
We will see another topic in our next post in the category of thermal engineering.

### Reference:

Engineering thermodynamics by P. K. Nag