TD-Class-5-Summary

MSubbu emphasized the importance of regular study time for GATE preparation, urging Jeevitha to allocate at least one hour daily despite her internship commitments. He stressed that time spent on study now cannot be accumulated later, and reminded her of her earlier commitment to the course. MSubbu also instructed the class on meeting etiquette, requesting participants to remain silent during class hours, ask questions by unmuting their microphones, and not turn on their videos.

MSubbu discussed phase equilibria, focusing on the criteria for phase equilibrium, which includes equality of chemical potential, pressure, and temperature for coexisting phases. He explained how to calculate the bubble composition using Raoult's law and the Antoine equation, given temperature, vapor pressure, and total pressure. The procedure involves solving for the mole fractions of the components in the vapor and liquid phases, ensuring the total mole fraction is one. MSubbu provided a step-by-step method to find the bubble composition, emphasizing the use of Antoine equation to calculate vapor pressure and then determine the mole fractions.

MSubbu explained the concept of phase equilibria in binary mixtures, focusing on the relationships between pressure, temperature, and composition. He described the dew line, which represents the pressure versus vapor composition for an ideal solution, and explained that the pressure versus temperature curve is linear. MSubbu also discussed steam distillation of immiscible liquid mixtures, noting that the boiling point of the mixture is lower than that of the pure components, and explained the concept of azeotropes.

MSubbu explained flash calculations, which determine vapor and liquid compositions and the relative amounts of vapor and liquid in a flashed mixture. He described the process of solving for the fraction of vaporized feed (V/F) and the vapor and liquid compositions using mass balances and equilibrium relationships. MSubbu emphasized that for simple problems, hand calculations can be performed, but more complex systems require computer tools like Excel.

MSubbu explained the concept of phase diagrams, particularly focusing on the behavior of liquids and vapors under different pressure conditions. He described how reducing pressure causes a liquid to vaporize, with the vapor containing more volatile components, and explained the use of tie lines to represent constant pressure conditions. MSubbu also covered the calculation of bubble and dew pressures, emphasizing that the operating pressure of a flash column should be between these two values. Finally, he discussed non-ideality in liquid phases, introducing the concept of activity coefficients and excess Gibbs free energy, and explained how to calculate these values from equilibrium combustion data for a methanol-water system.

MSubbu explained the calculation of activity coefficients and molar excess Gibbs free energy for binary mixtures, using the Margules one-parameter model. He demonstrated the method using an example of an azeotropic mixture of components A and B at 80°C, where the vapor and liquid compositions are equal at 50% each. 

MSubbu emphasized the importance of spending at least 1 hour daily on studying and logging the time spent to build confidence and improve exam performance. He also mentioned that tests for the covered portions and and other portions would be posted by the next day, and the course would move on to fluid mechanics by Friday.

MSubbu explained the application of Raoult's law and Henry's law to determine the equilibrium compositions of methane and water in a pressure vessel. He demonstrated how to calculate the mole fraction of methane in the liquid phase and water in the vapor phase using the given Henry's law constant for methane and vapor pressure of water. MSubbu emphasized the importance of correctly applying the laws based on the given constants and highlighted that choosing the wrong component to apply each law could lead to incorrect results.

MSubbu discussed reaction equilibrium, focusing on the essentials of the topic. He explained the relationship between Gibbs free energy, equilibrium constant, and temperature, noting that for exothermic reactions, the equilibrium constant decreases with increasing temperature. MSubbu also covered how to calculate the equilibrium constant at different temperatures using the Vant-Hoff expression which is analogous to Clausius-Clapeyron equation. He then moved on to discuss the calculation of equilibrium conversion, including the effect of pressure and temperature on exothermic reactions. Finally, MSubbu explained how to solve for the equilibrium constant in gas-solid reactions, noting that the activity of solids is taken as one unless otherwise specified.

MSubbu announced plans for upcoming classes, including a summary session on Wednesday covering 15 conceptual questions and a peer discussion session either tomorrow or Thursday, which will be finalized by 10 AM tomorrow. He emphasized the importance of students spending at least one hour daily studying, beyond the three hours of weekly classes, and mentioned that six tests have already been posted with three more to be added by tomorrow afternoon. The discussion concluded with updates about students' ranks and internships, including Surjya's GATE score of 983 and RanjanaShree's upcoming internship at CPCL.