TD-Peer Discussion - Session-3

Karthikeyan led a discussion session on thermodynamics, focusing on difficulties students face when solving problems. He emphasized the importance of understanding concepts and choosing the correct equations for different scenarios. Karthikeyan planned to work through thermodynamic problems from the GATE 2025 question paper during the session. He encouraged students to share their difficulties and questions, stressing the value of interaction for a productive session.

Karthikeyan discussed the concepts of excess properties, residual properties, and fugacity in solution thermodynamics, emphasizing the importance of understanding the theory behind these terms. He explained the differences between excess and residual properties, and how fugacity relates to the pressure of real gases. Karthikeyan also solved a problem involving the calculation of fugacity for a saturated vapor, using the concept of chemical potential at equilibrium.

Karthikeyan explained the Gibbs-Duhem equation and its application to a binary system, demonstrating how to solve for the mole fraction using given data. He emphasized the importance of understanding the theory and solving practice problems. The discussion then shifted to phase equilibria, with Srinithi expressing interest in moving on to that topic.

Karthikeyan explained the solution process for three thermodynamics problems involving mole fractions, vapor pressures, and activity coefficients. For the first problem, he demonstrated how to use Raoult's law to find the mole fraction at a given pressure and temperature. For the second problem, he showed how to use component balances and material balances to find the vaporized feed fraction. For the third problem, he explained how to calculate activity coefficients for a binary mixture of methanol and water at equilibrium, and then how to find the excess Gibbs free energy using those coefficients.

Arputhaselvi and Karthikeyan discussed the relationship between molar properties and excess Gibbs free energy, clarifying that the excess Gibbs free energy divided by RT is equal to the natural logarithm of the activity coefficient. They then explored a reversible exothermic gas-phase reaction, explaining how the rate constant varies with temperature and pressure, and how equilibrium conversion increases with pressure. Karthikeyan also explained how to derive and manipulate equations for Gibbs free energy in different reaction scenarios, emphasizing the importance of understanding stoichiometric coefficients and mole fractions.

Karthikeyan discussed the importance of understanding concepts and solving previous GATE questions to prepare for the exam. Arputhaselvi shared her experience with thermodynamic questions, emphasizing the need for strong conceptual understanding to choose the correct answers. Karthikeyan agreed and explained the importance of understanding processes like isothermal, isobaric, and isochoric, before moving on to solve a sample problem from the GATE2025 paper.

Karthikeyan explained how to solve a problem involving a real gas mixture, using Dalton's law and fugacity coefficients to find the total mixture fugacity. Arputhaselvi discussed a second problem about entropy change when partitions are removed between two gases at the same temperature and pressure, calculating the mole fractions and entropy change using given equations.

Karthikeyan explained a problem involving a spring and gas expansion, heat were added to the system, causing the gas to expand until the piston pressed against stoppers at 5 cm displacement. He guided the class through calculating the work done by expansion and the energy stored in the spring, which opposed the expansion work. Using the first law of thermodynamics and given values for specific heat capacity, the final temperature was determined to be 600 Kelvin.

Karthikeyan and Arputhaselvi discussed thermodynamics concepts, focusing on work done by gases and springs. They clarified that expansion work is done on the spring, not by it, and Karthikeyan suggested understanding various equations to solve thermodynamics problems. They then solved a problem involving an azeotrope, finding that the mole fraction of component A in the liquid phase is 60%. Karthikeyan advised against making mistakes in formatting answers and offered to share the PDF of the discussed material in the group (shall get the pdf from here).