( )
OR
( )
OR
( )
( )
⁄
For an ideal gas it has been shown that cp-cv=R. Thus cp/cv-1=R/cv ;and if
Then ⁄
⁄
, And hence
( )
From the ideal gas law
Thus
( )
( )
And hence
This is the relationship between the pressure and the volume of an ideal gas undergoing a
reversible adiabatic process.
Reversible isothermal pressure or volume changes of an ideal
gas:
From the first law of thermodynamics
As dT=0 (isothermal process),then
∫
dU=0 ,therefore
∫
Integrating between the state 1 and 2 gives
( )
( )
Thus for an ideal gas an isothermal process is one of constant internal energy during which
the work done by the system equals the h