Nature of Process

• The relationship between the pressure p and the volume V for any process undergone by a gas depends upon the nature of the process. A general relationship is usually expressed in the form of

                

  (2.8)

  
  This is an equation of state of a polytropic process. For a constant temperature (isothermal) process of an ideal gas, x= 1.

• If there is no heat transfer to or from the gas, the process is known as adiabatic. A frictionless adiabatic process is called an isentropic process and x equals to the ratio of specific heat at constant pressure to that at constant volume.

  The equation PV^x=constant can be written in a differential form as

  (2.9)

  
  

  Using the relations

  and	(2.10)
  	(2.11)

  We get

  
  Therefore, the compressibility K, or bulk modulus of elasticity E for gases depends on the nature of the process through which the pressure and volume change.

Fig 2.2 State Change of Perfect Gas

• For an isothermal process of an ideal gas (x = 1), i.e. E = p or K = 1/p .
  
  
• The value of E for air quoted earlier is the isothermal bulk modulus of elasticity at normal atmospheric pressure and hence the value equals to the normal atmospheric pressure.