The second law of thermodynamics often leads to expressions that involve inequalities; one of them is the Claussius inequality.

It states that, the cyclic integral of $\frac{dQ}{T}$ is always less than or equal to zero. This inequality is valid for all cycles, reversible or irreversible. i.e $\oint\frac{dQ}{T} ≤ 0$

Any heat transfer to or from a system can be considered to consist of differential amounts of heat transfer. Then the cyclic integral of $\frac{dQ}{T}$ can be viewed as the sum of all these differential amounts of heat transfer divided by the temperature at the boundary

The equality in the Clausius inequality holds for totally or just internally reversible cycles and the inequality for the irreversible ones.