# In dS≥dQ/T, material equilibrium means that there is not material changes at all or that a material change can be reversible and at equilibrium?

I am reading Levine's Physical Chemistry, I know how to arrive to that equation, but I have questions.

First, $$\mathrm{d}S=\mathrm{d}Q/T$$ for material equilibrium, but if there is a heat flow I understand that there is a reversible process going on, what kind of process can it be? Only a reversible thermal or mechanical process or also a reversible material change?

Second, the book says

$$\mathrm{d}S > \frac{\mathrm{d}Q_\mathrm{irrev}}{T} \qquad\text{and}\qquad \mathrm{d}S = \frac{\mathrm{d}Q_\mathrm{rev}}{T}.$$

Then states the equation $$\mathrm{d}S ≥ \mathrm{d}Q/T$$ and says $$\mathrm{d}S$$ equals $$\mathrm{d}Q/T$$ for a reversible process and $$\mathrm{d}S$$ is greater than $$\mathrm{d}Q/T$$ for an irreversible chemical reaction or phase change.

I imagine that the heat flow is different if the process is reversible or irreversible and that the equation $$\mathrm{d}S≥\mathrm{d}Q/T$$ takes into account that the $$\mathrm{d}Q$$ is different, is this correct? I think I am a little confused just because there are no more subscripts in $$\mathrm{d}S≥\mathrm{d}Q/T$$.

Also, I think that the heat flow due to a irreversible process is greater than the heat flow due to a reversible process that goes to the same states, why is that?

• Here is a tutorial to help you understand the change in entropy for a system experiencing an irreversible process and application of the Clausius inequality: physicsforums.com/insights/grandpa-chets-entropy-recipe – Chet Miller Jan 15 at 12:23
• In the inequality, the T is not the system temperature (which can vary from location to location within the system for an irreversible process). The T here is the temperature at the interface between the system and the surroundings where the heat transfer is occurring. – Chet Miller Jan 15 at 12:25