Table of Contents

**Pure substance:**

A system is said to be composed of pure substance if

- Homogenous in composition.
- Homogenous in chemical aggregation.
- Invariable in chemical aggregation.

**State postulate:**

Two independent thermodynamics properties are sufficient to establish a stable thermodynamic state of a system of pure substance. For example:

T = T ( P ,V ) where T= temperature , V= volume , P= pressure

Two independent intensive thermodynamics properties are sufficient to establish a stable thermodynamics state of system of a pure substance.

u = u( P,v ) where u= specific internal energy and v= specific volume

**Ideal gas
and its relationship:**

**Boyle’s law**

It state that volume of given mass of gas is inversely proportional to the pressure when temperature is constant.

V** **∝
1/P

PV = constant

P_{1}V_{1} = P_{2}V_{2}

**Charles law:**

It is also known as Gay – Lussac’s law. It give two statement that is given below:

If pressure is constant then volume is directly proportional to the temperature. It is given by:

V ** **∝ T

V = KT where k is constant

And if volume is taken constant then pressure is directly proportional to the temperature. It is given by:

P ** **∝ T

P = KT

Where K is constant.

**Equation of state:**

## Two phase ( liquid and vapor ) mixture system

**Saturation curve on T – v diagram **

Consider a frictionless piston cylinder device , shown in figure containing a some amount of water at atmospheric condition. If the weight of piston is negligible pressure remains constant at 1 atm throughout the process.

When heat is supplied to the system then from external source. The temperature of water is increase then specific volume is also slightly increase which is represented by 12 which is called compressed liquid. When temperature reaches 100 **°C** then it just start to evaporate in this state called saturated water and it is shows by 2. Then, water temperature and pressure remains constant but volume is increase due to intermolecular expansion. It is represented by state 24 in this state water completely converted vapor by absorption of latent heat. Then this state 4 called saturated vapor. Then, when temperature increase specific volume of water also increase which is represented by 45 and it is called superheated vapor. If similar heating process is carried out in higher pressure then evaporation takes place at higher temperature then length of the 24 is decrease in one higher pressure the saturated vapor and saturated liquid is occur at same point the point is called critical point. In this point the properties of saturated liquid and saturated vapor be identical.

**Saturation curve on p- v diagram:**

Consider a frictionless piston cylinder device which contain a certain amount of water at 100 **°C **it remains constant then if the external force of cylinder reduced slowly then its pressure decrease but specific volume increase slightly which is represent by 12 called compressed liquid. When pressure reach 1 atm then start to evaporate represent by 2 then called saturated liquid. Then, temperature and pressure remains constant but volume increase represent by 24 called saturated mixture. Then, when evaporation complete this point represented by 4 and called saturated vapor. Then, pressure is decrease but specific volume is increase represented by 45 called superheated vapor as shown is figure below.

When temperature is increase then evaporation takes place at higher pressure then length of 24 is decrease but at one temperature the saturated vapor and saturated water is exist same point called critical point and in this time the properties of saturated liquid and saturated vapor is identical.

**Remember given terms definition:**

**Saturation pressure**: at given temperature the
pressure at which phase change(liquid to vapor or vapor to liquid) occurs is
called a saturation pressure. If water 100**
°C **then evaporation is starts at 1atm pressure in this condition saturation
pressure is 1 atm.

**Saturation temperature**: at given pressure the temperature at which phase change(liquid to vapor
or vapor to liquid) occurs is called a saturation temperature. If water
pressure 1 atm the evaporation starts at 100**
°C **then the saturation temperature is 100** °C.**

**Saturated liquid**: it is the state where substance
evaporation just starts during heating or condensation just complete during
cooling is called saturated liquid.

**Saturated vapor** : it is the state where substance
evaporation just completes during heating or condensation just starts during
cooling is called saturated vapor.

**Compressed liquid**: when the saturated liquid is further
cooled or compressed called compressed liquid.

**Superheated vapor** : when the saturated vapor is further
heated or expand called superheated vapor.

**Degree of superheat**: it is a temperature difference between
temperature of superheated vapor and temperature of saturation called degree of
superheat.

**Critical point**: it is state of substance when saturated liquid and saturated vapor exist same point and properties of saturated liquid and saturated vapor is identical called critical point.

**Quality:**

It is a ratio of mass of saturated vapor and total mass of the two phase mixture. It is denoted by x. and given by:

x = m_{g}/m

x = m_{g}/m_{g}+m_{l}

where m_{g} is mass of
saturated vapor and m_{l} is mass of
saturated liquid.

**NOTE: Quality is always varies from 0 to 1. Quality of
saturated liquid is 0 and saturated vapor is 1. Then at critical point quality
is 0.**

**Moisture content**:

it is a ratio of mass of saturated liquid to total mass of two phase mixture. It is denoted by y. and give by:

y = m_{l}/m

**relation of x and y** : y = 1- x

**Relationship between properties of two phase mixture:**

We know specific volume is ratio of total volume to mass so

therefor it is a required expression for properties of two phase mixture.