Thermodynamics and Heat Engine4 (3+1)

LESSON -3 WORKING FLUID, GAS AND VAPOUR AND GAS LAWS

Example: Fig. 3.1 shows an example of working fluid in different devices used in a steam power plant:

• Liquid and vapor in boiler

• Vapor in a steam engine or steam turbine,

• Liquid in feed water pump,

• Liquid and vapor in condenser/heat exchanger

• Gas in furnace etc.
  

Fig. 3.1. Working fluid in different components of a steam power plant

3.2. GAS AND VAPOUR

A gas is the name given to the state of any substance of which the evaporation from the liquid state is complete. Within the temperature limits of applied thermodynamics such substances as oxygen, nitrogen, hydrogen, air, etc., may be regarded as gases.

From engineering point of view, a vapour may be defined as a partially evaporated liquid, and consists of the pure gaseous state together with particles of liquid in suspension. It does not behave in the same way as a gas, as the substance is liable to further evaporation or condensation on changes of temperature and pressure. The laws of gases do not apply to vapours. When a vapour becomes completely evaporated it is said to be dry, and any further heating of a dry vapour is termed as superheating. Once a vapour is superheated it behaves approximately as a gas. The vapours commonly used in engineering practice are steam, carbon dioxide, sulphur dioxide and ammonia.

 In the following lessons gases and vapours will be treated separately; the student is warned to distinguish between vapour and gases.

3.3. GAS LAWS

A gas which strictly obeys Boyle’s law and Charles’s law is called a perfect gas or an ideal gas.

The combination of Boyle’s law and Charles’s law can be expressed by means of a simple equation known as Characteristic equation of gas, also called Ideal gas equation.

In strict sense, no gas which exists in nature is perfect. But all gases are treated as ideal gases because they obey gas laws as pressure approaches to zero (p 0).

Many gases such as air, Oxygen, Nitrogen, Hydrogen, Helium, Carbon dioxide, etc., are treated as ideal gases as they obey gas laws with sufficient accuracy at normal temperature and pressure.

3.3.1. Boyle’s Law

 When temperature remains constant, the volume of a perfect gas is inversely proportional to the absolute pressure

 where

p = absolute pressure of gas

       V = volume of a gas at pressure p.

       T = absolute temperature of gas.

c = constant of proportionality.

or      pV = constant

This tells that when temperature remains constant, the product of absolute pressure and volume of a given quantity of a gas is constant.

Boyle’s Law for change of state: Refer Fig. 3.2. If the gas is made to change its state from state 1 to state  2, without change in its temperature, then   p1V1 = p2V2   or   or           (per unit mass basis) where, v is specific volume of a gas at pressure p, m3/kg

Fig. 3.2. Boyle’s Law on p-V diagram

3.3.2. Charles’s Law

It may be stated in two ways:-

(a)  If pressure remains constant the volume of a given mass of gas varies directly as the absolute temperature.

Charles’s Law for change of state: (Fig. 3.3)  If process occurs between from state 1 to state 2, then

Fig. 3.3. Charles’s Law on V-T diagram

(b) If the volume remains constant, the pressure of a given mass of gas varies directly with temperature.

           

    If the process occurs between two states

                       

3.3.3. Characteristics equation of gas (Ideal gas equation)

 For a fixed mass ‘m’ of an ideal gas the product of absolute pressure and volume is proportional to its absolute temperature.

 Thus,    PV = m R T           ………………..(3.1)

     where,  p = absolute pressure of gas, N/m²

                   V = Volume of gas, m³

                   T = absolute temperature of a gas, K

In the above equation ‘R’ is known as characteristic equation of perfect/ideal gas and is called the characteristic gas constant or specific gas constant. It is different for different gas. Unit of R is  J/kgK   or  KJ/kgK

 For unit mass of a gas, the equation (3.1) can be written as

          pv = RT

   

               where, v is the specific volume of a gas at pressure p, in m³/kg =

Because, number of moles, n =     kgmole

or      m = n M

Then from equation (3.1) in terms of moles we can write

         PV = n (MR)T      

The product MR represented by R_U ( )  is known as the Universal Gas Constant. The value of R_U = 8.314 kJ/kgmole K = 8314 J/kgmole K.

Therefore,    PV  = n R_U T

Ideal gas equation for a change of state

 If a process occurs from state 1 to state 2, then