Wednesday, August 17, 2011

Clausius Inequality

           The Clausius inequality state that whenever a closed system undergoes a cyclic process, the cyclic integral of &Q/T is less than zero for an irreversible cyclic process and equal to zero for a reversible cyclic process. Mathematically,
                                          infinity&Q/T < 0, for an irreversible cyclic process
                                          infinity &Q/T = 0, for a reversible cyclic process
   combining the equations is written as
                                                            infinity -< 0
The Clausius inequality not only gives mathematically expression to the second law of thermodynamics, but it also gives the quantitative measure of irreversibly of the system. For example, the equation for an irreversible cyclic process may be written as,
                                                   infinity &Q/T + 1 = 0
Where 1 represents the amount by which the given cyclic process irreversible. When 1 is equal to zero, then the given cyclic process will be reversible. Moreover, a cyclic process in which infinity dQ/T is more then zero, is impossible because it violates the second law of thermodynamics.