Editing Second law of thermodynamics (section)

=== Entropy ===
{{main|Entropy (classical thermodynamics)}}
According to the [[Clausius theorem|Clausius equality]], for a ''reversible process''
: <math>\oint \frac{\delta Q}{T}=0</math>

That means the line integral <math>\int_L \frac{\delta Q}{T}</math> is path independent for reversible processes.

So we can define a state function ''S'' called entropy, which for a reversible process or for pure heat transfer satisfies
: <math>dS = \frac{\delta Q}{T} </math>

With this we can only obtain the difference of entropy by integrating the above formula. To obtain the absolute value, we need the [[third law of thermodynamics]], which states that ''S'' = 0 at [[absolute zero]] for perfect crystals.

For any irreversible process, since entropy is a state function, we can always connect the initial and terminal states with an imaginary reversible process and integrating on that path to calculate the difference in entropy.

Now reverse the reversible process and combine it with the said irreversible process. Applying the [[Clausius inequality]] on this loop, with ''T''<sub>surr</sub> as the temperature of the surroundings,
: <math>-\Delta S+\int\frac{\delta Q}{T_\text{surr}}=\oint\frac{\delta Q}{T_\text{surr}} \leq 0</math>

Thus,
: <math>\Delta S \ge \int \frac{\delta Q}{T_\text{surr}}</math>

where the equality holds if the transformation is reversible. If the process is an [[adiabatic process]], then <math>\delta Q=0</math>, so <math>\Delta S \ge 0</math>.