**Pure Substance and State Postulates**

**Pure Substance:**

A substance that is used as the working medium in thermodynamic is considered as the pure substance, and if the system consists of the substance having the following properties then it is said to be the system with pure substance;

**Homogeneity:**this means that the composition should be the same throughout the system.**Unchangeable chemical composition:**this means that the chemical composition should remain the same irrespective of the time.**Uniform chemical aggregation:**this means that the constituent particles should be integrated in a similar manner

**State postulate:**

If the system is composed of a pure substance, then thermodynamic properties of the pure substance can be determined by using the two given independent thermodynamic properties which are said to be the state postulate. For example, by using the pressure and volume of the substance for any state, we can determine the temperature of that substance at that state using the relation of pressure and volume.

We can also define the state postulate with the help of ** intensive properties** as ‘Two independent intensive thermodynamic properties are enough to determine the stable state of thermodynamic of the pure substance. For example, the temperature of the pure substance can be determined using the specific volume and pressure for any state. For example, temperature and specific volume are always independent.

**Ideal Gas and Ideal Gas Relation**

**Ideal gas:**

It is the hypothetical gas which follows the gas law at all the pressure and temperature condition whose molecules does possess any force of attraction. However, these molecules possess the interaction of elastic collision with each other or with the container’s wall.

In reality, this type of gas does not occur, but the gas at high temperature or low pressure tends to acts as the ideal gas because the distance between the molecules is greater at this conditions due to which the force tends to be low. This condition, i.e. pressure and temperature, varies according to the different gases.

**Viable conditions of ideal gas assumption;**

Assumption of an ideal gas is valid when the density of the gas is low having the negligible volume of gas particles, potential energy between the particles is low and when the particles of a gas behave independently of one another.

**Conditions at which the ideal gas can be used are;**

- Very low pressure
- Very high temperature
- Low density

**Relation of an ideal gas**

To understand the relation of gas first, we should be familiar with the three different laws which are explained as below;

**Boyle’s Law**

It states that if the temperature is constant, then the volume of the given mass of gas possess an inverse relationship with the pressure of that given mass of that gas, i.e. or

V∝1/P or PV= constant

**Charles’s Law:**

It states that if the pressure is constant, then the volume of the given mass of gas possess a direct relation with the absolute temperature of that given mass of the gas, i.e.

V∝T

**Gay-Lussac’s Law:**

It states that if the volume is constant, then the pressure of the given mass of gas possess a direct relation with the absolute temperature of that given mass of the gas, i.e.

P∝T

If we combine Boyle’s and Charles’ laws, then we can determine the relationship between pressure, volume, and temperature. For this let us suppose the unit mass of ideal gas undergoes the constant pressure process from state 1 to* i *which is followed by the constant temperature process *i* to 2 as shown in the figure;

**Applying Charles’s Law in 1 to i state, we get,**

V_1/V_i =T_1/T_i

V_i=T_i/T_1 *V_1

V_i=T_2/T_1 *V_1 ……… (1)

**Applying Boyle’s law for process i to 2, we get,**

V_2/V_i =P_i/P_2

V_i=P_2/P_i *V_2

V_i=P_2/P_1 *V_2 …….. (2)

Then equating equation 1 and 2 we get,

(P_1 V_1)/T_1 =(P_2 V_2)/T_2 …….. (3)

If there are more states, then the above equation follows;

(P_1 V_1)/T_1 =(P_2 V_2)/T_2 =(P_3 V_3)/T_3 =PV/T=R

PV=RT ……… (4)

Where R = gas constant for given gas and is called characteristics of gas constant having the unit as J/kg.K

The above equation 4 is for unit mass, so for ‘m’ kg of gas equation (4) can be written as;

PV=mRT …… (5)

Only getting the knowledge about the gas law is not enough because while implementing the gas law, we should be sure that we are using the correct units of the thermodynamic properties.

For example, if you are using the value of gas constant as 8.31 J/K Mol, then it is necessary to use pressure as Pascal, volume as cubic meter, and temperature as Kelvin. However, if you are using the value of R as 0.082 L. atm/K.Mol then pressure should be used in atm, volume in liters, and temperature in Kelvin.

**The behavior of the Pure Substance (Phase Change Processes):**

The following diagram will help us to understand the different behavior of the pure substance, i.e. solid, liquid, and vapor.

From the above diagram, it can be seen that the point where the solid, liquid and vapor phases occur together is said to be the triple point. Similarly, the point at which the liquid ad vapor is no distinguishable is said to be the critical point.

When the heat is given to the solid phase and reached the melting point, then the solid starts to convert into the liquid above the melting point which can be seen in the figure above. On further heating the liquid substance then the vaporization occurs converts the liquid into the vapor phase.

**Saturation curve on T-V diagram:**

Let us consider the piston-cylinder system having a certain amount of water at the atmospheric condition. If the piston’s weight is neglected, then the pressure in the system remains throughout the process. When the heat is supplied in the system at the constant pressure, then the temperature increased inside the cylinder, which interns increase the volume. This process will continue until the temperature becomes 100^{0}C. On further increasing the heat, then it would cause the evaporation.

During the evaporation process, the temperature and the pressure remain constant while the specific volume increases because of the intermolecular expansion of the substance. When the latent heat is completely absorbed then the liquid is converted into the vapor state which is said to be the saturated vapor phase. If further the heat is supplied to the saturated vapor than the specific volume increases with the increase in the temperature of the saturated vapor, thus reaching the superheated vapor.

The above-described process can be illustrated with the help of the following piston-cylinder diagram and T-v diagram;

In the figure4, the number 1 to 5 states the following phase transformation of the substance;

- Solid
- Mixed phase of solid and liquid
- Sub-cooled or compressed liquid
- Wet vapor, i.e. saturated liquid-vapor mixture
- Superheated vapor

When the heating process is performed on higher pressure instead of keeping the pressure constant by applying the weight on the piston, then the evaporation process occurs at a greater temperature which decreases the length of the straight horizontal line and becomes zero at particular pressure state which is said to be the critical point at which the properties of the saturated liquid and saturated vapor become identical.

The line joining the saturated liquid states is said to be saturated liquid line while the line joining the saturated vapor states is said to be saturated vapor line. Region to the left of the saturated liquid line is said to be sub-cooled liquid region and region to the right is said to be superheated vapor region while the region within the curve is said to be the region of the two-phase mixture.

The above-explained regions are shown in the figure given below:

**Saturation Curve on P-V Diagram**

Let us consider the piston-cylinder system having water at the sub-cooled state, which is in contact with the heat source having the temperature greater than that of the water where the piston is subjected to the external force. When the applied force from the piston is slightly reduced, keeping the temperature at 100^{0}C, then the pressure will decreases, which in term increases the specific volume. This process will occur continuously until the pressure reaches the atmospheric pressure (1 Atm.) then the water will reach the saturated liquid state.

And, evaporation process occurs when this saturated liquid takes heat from the source thus increasing the specific volume till it reaches the saturated vapor state where the temperature and pressure remain constant which is indicated by the straight horizontal line in the P- v diagram.

Further, the volume increases if the pressure is further reduced. This whole process can be illustrated in the P-V diagram as shown;

If the above process is repeated by increasing the temperature, then the evaporation occurs at the higher pressure which decreases the length of the straight horizontal line and becomes zero at particular temperature making the properties of saturated liquid and saturated vapor identical which is shown in the figure:

Like in the T-v diagram we can also show the two-phase mixture region in the P-v diagram as below;

**Different terms used in the Two-phase mixture system:**

**Saturation temperature**: The temperature at which the liquid is converted to vapour or vapour to liquid is said to the saturation temperature for a given pressure. For example, if the water is heated at atmospheric pressure, then evaporation of water occurs at 100^{0}C, which is the saturation temperature for atmospheric pressure.

**Saturation pressure**: The pressure at which the vapour to liquid or liquid to vapour occurs, that pressure is said to be saturation pressure. For example, if the water is expanded at 100^{0}C, then the evaporation of the water takes place at one atmospheric pressure which is the saturation pressure.

**Saturated liquid:**It is the phase at which the condensation just complete during the cooling or evaporation just starts during heating.

**Saturated vapour**: It is the phase at which the evaporation just complete during heating or condensation just start during cooling.

**Sub-cooled liquid:**If the saturated liquid is further compressed then the liquid is said to be sub-cooled liquid.

**Superheated vapour:**If the saturated vapour is further heated then the vapour is said to be superheated vapour.

**Degree of superheat:**It is the difference in temperature between the saturated vapor and the corresponding saturation temperature.

**Quality:**

It is the ratio of the mass of saturated vapour to the total mass of the two-phase mixture. It is also known as the dryness factor which is denoted by x. if m_{g} is the mass of saturated vapour and m is the total mass of the mixture then quality(x) is given as;

x=m_g/m=m_g/(m_l+ m_g ) …….. (6)

Where, * m1*= mass of saturated liquid

From the above relation it is clear that the value of quality of dryness factor varies from 0 to 1 within the region of saturation as shown in the figure below;

**Moisture Content:**

It is the ratio of the mass of saturated liquid to the total mass of the two-phase mixture and denoted by ‘y’ which is given as;

y=m_l/m=m_l/(m_l+ m_g )=1-x …….. (9)

**Specific properties of two-phase mixture:**

It can be expressed in terms of the dryness factor or quality. As the specific volume of the two-phase mixture is the ratio of the total volume of the mixture to the total mass of the mixture which is given as;

v=V/m=V_l/m+V_g/m ……. (10)

Where, V_{l} = volume of saturated liquid, V_{g} = volume of saturated vapour

The above equation (10) can be expressed in terms of quality as given below;

v= V_l/m_l m_l/m+V_g/m_g m_g/m= v_l (1-x)+v_g x

v_l+(v_g-v_l )x=v_l+xv_lg ……. (11)

Where,

Like specific volume other thermodynamic properties can also be express in terms of quality of dryness factor which are given as below;