[Physics] Why must heat supplied in the definition of entropy be reversible? Can’t it be irreversible after all it is a state function


The definition of entropy contains the term $Q_\text{rev}$ which means the heat supplied or taken out reversibly. I thought yes it can be after all only the initial & final states are important as entropy is a state function irrespective of the process heat is transferred. However I was baffled when I first read Clausius' theorem where it is written that $dS \geq \dfrac{Q}{T}$. If $Q$ is transferred irreversibly, then $dS$ is greater than $\dfrac{Q_\text{irrev}}{T}$; if the heat transfer is reversible, then only $dS$ equals $\dfrac{Q_\text{rev}}{T}$. So, does that mean entropy depends on the process heat energy is transferred?? Then, how can it be a state function? Where am I mistaking? Please explain.

Best Answer

Suppose you start with a system in some state $P_1, V_1, T_1$ and you add some quantity of heat $\Delta Q$ to it so the system changes to a different state $P_2, V_2, T_2$. The final state will depend on how you added the heat $\Delta Q$. Adding the heat $\Delta Q$ in a reversible process will result in different values for $P_2, V_2, T_2$ compared with adding the same amount of heat $\Delta Q$ in an irreversible process.

Entropy is indeed a state function, so if you know $P_2, V_2, T_2$ you can calculate the entropy change. Since reversible and irreversible processes will result in different values for $P_2, V_2, T_2$ they will also result in different values for the entropy change.