Question

As temperature increases toward the critical temperature, the values of v_f and v_g become more far away from each other.

Answer 1

It is because the properties of liquids (saturated or subcooled) are more affected by temperature than they are by pressure.

To illustrate, I provide you the following properties, calculated using some examples:

State 1: Pressure 100 kPa, Temperature 25 C

Enthalpy 104,8 kJ/kg, volume 0,001003 m³/kg

State 2: Pressure 100 kPa, Temperature 10 C

Enthalpy 42,08 kJ/kg, volume 0,001 m³/kg

State 3: Pressure 500 kPa, Temperature 25 C

Enthalpy 105,2 kJ/kg, volume 0,001003 m³/kg

State 4: Pressure 500 kPa, Temperature 10 C

Enthalpy 42,47 kJ/kg, volume 0,0010001 m³/kg

• As you can see, when the pressure was increased by 500% the specific volume was increased by 0,01% and the enthalpy by less than 1%.
• When the temperature was increased by 15 degrees, or 5% in Kelvin, the enthalpy more than doubled and the volume was increased by 0,3%. 30 times more than the caused by the increase in pressure.

However, I don’t really know why temperature has a more significative influence over liquid’s properties. I suppose its related to thermal dilation, which probably is more significant than the compression of already close particles. I’m not positive, though. All I know is that liquids are more sensitive to temperature than they are to pressure.

Two more states:

State 5: Pressure 10000 kPa, Temperature 10 C

Enthalpy 51,69 kJ/kg, volume 0,0009956 m³/kg (volume decrease)

State 6: Pressure 10000 kPa, Temperature 150 C

Enthalpy 638,2 kJ/kg, volume 0,001053 m³/kg (volume increased in spite of the 100 bar pressure!)

When looking at a graph of comparing temperature and specific volume, we see that for increasing pressures, the boiling point increases and that the length of the saturated liquid-vapor line decreases.

I understand this as because of an increase in pressure, molecules are harder to push apart (as essentially pressure is an external force keeping the molecules together).

The way I understand it is that because we needed a higher boiling point at high pressures, we've already inputted a lot of energy to get to this point, and so the specific volume of the liquid is already quite high for higher pressures, as inputting energy essentially tries to push apart these molecules. Hence, to reach the saturated vapor point, we don't need as much energy to keep forcing particles apart (so the increase in specific volume is not as much).

Fig :- graph between temperature and specific volume

The graph represents temperature vs. specific volume for a pure component. Because this is a pure component, several facts are known:

1) In order to gather the given data, some container was partially filled with a given liquid, with the remainder of the container filled with the vapor of the same substance. The container contained a substantial fraction of liquid and a substantial fraction of vapor (e.g., 50% liquid and 50% vapor), to ensure that some liquid and some vapor remained in the container as the liquid temperature was increased.

2) The liquid density goes down (liquid specific volume increases) as the liquid temperature increases.

3) There is a relationship between the temperature of the liquid and the pressure inside the container. This relationship is determined by the vapor pressure of the liquid, which can be calculated by the Antoine equation. As the temperature inside the container goes up, the vapor pressure of the liquid goes up. As a result, more liquid goes into the vapor phase, and since this is a closed container, the pressure in the container goes up as a result. As the pressure increases, the density of the vapor phase goes up (vapor specific volume decreases).

4) At some point, as the temperature increases, the liquid density decreases enough to equal the vapor density, and the critical point is reached. At this point, there is only one phase in the container, as the liquid and vapor phase densities are equal.

Because increasing temperature causes liquid specific volume to increase, and at the same time causes vapor specific volume to decrease due to the dependencies between temperature, vapor pressure, and specific volume, the width of the saturated liquid-vapor line decreases as temperature increases, until you reach the critical temperature.