# Review the Principle of Increasing Entropy

dQ < 0 is possible
ΔS < 0 is possible
In Lesson 7C, we introduced the concept of entropy generation, Sgen.
Here is a brief summary of what we learned in that lesson:
Internally reversible processes:
Irreversible proceses:
We concluded that:
Note:
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### Ch 8, Lesson A, Page 2 - Review the Principle of Increasing Entropy

• Let’s take a moment here to review the principle of increasing entropy.
• First of all, because entropy is a state variable or property, ΔS between two states is the same regardless of whether the path that a process follows between the states is internally reversible or irreversible.
• The catch is that the only direct way to EVALUATE DS is by integrating dQ over T along an internally reversible path.
• If we tried to evaluate the integral of dQ over T along an irreversible path, we would get a value that is LESS than if we had followed an internally reversible path.
• Therefore, ΔS is greater than the integral of dQ over T for an irreversible process.
• This is the key to understanding entropy generation and entropy balances.
• Sometimes it is convenient to combine the equality for internally reversible processes and the inequality for irreversible processes to write one inequality that applies for ALL processes.
• The result is that ΔS for any process is greater than or equal to the integral of dQ over T along the process path.
• OK.  Here I would like to dispel a common myth.  Some students think that entropy never decreases.  That is not correct.
• If we transfer heat OUT of a system in a process, then dQ is negative and ΔS  can also be negative.  Transferring heat from a system that undergoes an internally reversible process ALWAYS reduces the entropy of the system.
• Of course, we can transfer heat into a system as well.  In that case, ΔS is positive and the entropy increases.
• I hope this is clear.
• Alright then, inequalities are always tough to work with, so let’s make this equation into an equality.
• Flip the page to see how.