TD-Peer Discussion - Session-2

MSubbu encourages the class to be more interactive and suggests using simple English to accommodate non-Tamil speaking students. He welcomes a new student, RanjanaSri, who is joining despite ongoing exams. Karthikeyan takes over the session, experiencing some connectivity issues, and asks Srinidhi to share their screen.

The session focused on thermodynamics concepts, particularly Carnot engines and refrigerators. Karthikeyan explained the efficiency formula for heat engines and refrigerators, emphasizing that the Carnot engine has the maximum efficiency. He solved a sample problem from GATE2020 to illustrate the application of these concepts. 

Karthikeyan explained a thermodynamic problem involving two engines in series, where heat is extracted from a thermal reservoir at 400 Kelvin and discarded to cold reservoirs at 360 and 300 Kelvin. He calculated the work extracted from each stage, finding 0.2 kilowatts for the first stage and 0.3 kilowatts for the second stage, resulting in a total work output of 0.5 kilowatts. According to the problem, this work output represents 50% of the corresponding Carnot efficiency, leading to a final answer of 0.25 kilowatts.

Karthikeyan explained two thermodynamics problems involving entropy changes. In the first problem, he described mixing 10 kg of water at 300 Kelvin with 10 kg of water at 350 Kelvin, resulting in a final temperature between 300 and 350 Kelvin due to the irreversible nature of the process. In the second problem, he discussed the freezing of one mole of benzene, calculating the entropy change using the heat of fusion and the given temperatures of 5.5 Kelvin for benzene and 0°C for the ice bath. Karthikeyan clarified that the reference temperature of 0 Kelvin is used for ease of calculation, and he encouraged participants to ask questions if they had any doubts.

Karthikeyan led a discussion on solving thermodynamic problems, focusing on finding the entropy of a mixture and calculating the final temperature in a thermodynamic cycle. He explained the steps to determine the volume of vapor, mass fraction, and entropy using given data. Arputhaselvi raised a question about the temperature calculation, which Karthikeyan acknowledged as a good point for further discussion. They also briefly touched on using Mollier diagrams and the importance of reading questions carefully when solving thermodynamic problems.

Karthikeyan explained the process of finding enthalpy and entropy changes using thermodynamic equations and Maxwell relations. He demonstrated how to transform variables, apply constants, and integrate to find the desired changes. For the final question, he showed how to convert a PV diagram to a TS diagram and calculate entropy changes using constant volume and pressure processes. The answer to the last question was determined to be B.

Karthikeyan explained concepts related to entropy, pressure, and volume changes in thermodynamics, emphasizing the increase in entropy with increased pressure at constant volume. He demonstrated how to calculate partial molar volumes and the volume change of mixing using mole fractions and provided an alternative method using compatibility factors. Karthikeyan also discussed the compressibility factor and residual properties of real gases, explaining how to derive and calculate the gas compressibility coefficient using given formulas and data.

Karthikeyan explained the method to solve a thermodynamics problem involving the fugacity of a saturated liquid, emphasizing the importance of understanding the underlying concepts before attempting to solve complex equations. He advised the class to focus on managing time during exams by tackling easier problems first and leaving more challenging ones for later. Karthikeyan also stressed the significance of understanding terms like fugacity, activity coefficients, and residual properties in solution thermodynamics.