Quantifying Irreversible Entropy Change in Adiabatic Gas Expansion: A Comprehensive Analysis

we calculate the entropy change for irreversible adiabatic expansion for real gas that does not mention in most Physical Chemistry textbook. This often prompts undergrad students, who are customized to study the behavior of real gas and ideal gas in thermodynamic course, to ask about the entropy change in real gases when they are subjected to expand. Change in temperature is also very important in this regard. So how will a student determine the entropy change for irreversible process? This procedure is quite simple according the textbooks. We cannot directly apply the equation ∆S = S2 – S1 = ∫_i^f▒(đQ_rev)⁄T as for irreversible process ∆S may not be necessarily equal to ∫_i^f▒(đQ_irrev)⁄T . Although entropy is a state function, it does not depend on the path how the system changes its course to achieve the final state. First, we have to identify the initial and final states and then find a suitable reversible pathway for the course. The calculations of ideal gases for irreversible pathway are done in textbooks. However, students need to know for the real gases formulas for the entropy change so that one’s expectation matches with the experimental values when done in practical. Here we considered the calculations for irreversible adiabatic expansion (normal and free) and what happens to the temperature of the system when it achieves the final state.