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

and

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.

infinity&Q/T < 0, for an irreversible cyclic process

infinity &Q/T = 0, for a reversible cyclic process

and

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.