TD-Class-4-Summary

The class began with administrative instructions and expectations for student behavior during lectures. The main portion of the class covered various thermodynamic concepts including energy balance problems, the Joule-Thompson coefficient, and fundamental relationships between temperature, pressure, and enthalpy. The session concluded with discussions on steam turbine calculations, entropy change of mixing, partial molar volumes, and residual properties in thermodynamics, with emphasis on practical applications and mathematical methods for solving thermodynamic problems.

MSubbu welcomes students to the class and discusses the learning management system features, including the ability to mark content as completed. He explains that the course will cover 70% of core chemical engineering subjects by August 14th, excluding mathematics and general aptitude, which will be addressed later. MSubbu outlines class expectations, including remaining silent during the lecture, not turning on video, and asking questions during designated times. He concludes by starting the class with a 30-second silent prayer.

The discussion focuses on an energy balance problem involving air flow from a pipeline to a receiver tank. MSubbu explains that the final temperature of the air in the tank differs from the source temperature due to energy considerations. He walks through the energy balance equation, simplifying it by neglecting kinetic and potential energies and considering the tank initially empty. The problem is solved using ideal gas relationships, resulting in the final temperature of the tank contents being equal to gamma (the ratio of specific heats) times the source temperature.

MSubbu explains the concept of the Joule-Thompson coefficient, which measures the temperature change of a gas when it undergoes a pressure drop through a small opening like a capillary tube or needle valve. He notes that this process occurs at constant enthalpy. MSubbu then begins to discuss how to calculate this coefficient using an equation of state for a non-ideal gas, given specific values for constants and initial conditions of temperature and pressure.

MSubbu explains the cyclic relation rule for variables T, P, and H, and discusses how to derive various thermodynamic relationships. He uses a mnemonic diagram to illustrate energy relations and Maxwell relations. MSubbu then demonstrates how to calculate specific partial derivatives using the given equation of state, emphasizing the importance of unit consistency. The discussion focuses on fundamental thermodynamic concepts and their mathematical representations.

MSubbu explains the importance of unit consistency in thermodynamic calculations, particularly when dealing with pressure units and Joule-Thompson coefficients. He then introduces a problem involving steam turbine power calculation using steam table data, focusing on determining the quality of steam at the turbine exit after isentropic expansion. MSubbu describes how to represent the process on a temperature-entropy diagram and explains the method to calculate the steam quality using entropy values for saturated liquid and vapor states.

MSubbu explains how to calculate the power produced by a turbine using the mass flow rate and change in enthalpy. He discusses the differences between reversible adiabatic and irreversible adiabatic processes, noting that the power produced in the irreversible case is typically 10-20% higher. MSubbu then moves on to explain steady flow compression, emphasizing the use of the integral of VdP for flow processes instead of -PdV for closed systems. He concludes by highlighting that for a flow compressor, the work will be gamma times the work of a closed system.

MSubbu discusses the calculation of entropy change of mixing for ideal gases using a problem from Smith and Vanness. The problem involves mixing nitrogen and argon at different initial temperatures and pressures. MSubbu explains the steps to calculate the final temperature, pressure, and volume of the mixture, as well as the entropy change. He emphasizes that the entropy change of mixing is always positive, indicating that energy must be spent to separate the components. MSubbu also mentions that simpler calculations can be used if the initial conditions are the same for both gases.

MSubbu explains how to calculate partial molar volume from a given molar volume expression. He demonstrates the graphical method of finding partial molar volume by drawing tangents on a molar volume vs. composition plot. The intercepts of these tangents at x1=1 and x2=1 give v1-bar and v2-bar, respectively. MSubbu then derives the equations for v1-bar and v2-bar algebraically, relating them to the slope of the tangent line. He also discusses how to calculate partial molar volume at infinite dilution and volume change of mixing.

The professor discusses residual and excess properties in thermodynamics, focusing on the calculation of residual Gibbs free energy. He explains how to derive expressions for residual properties using the truncated virial equation of state with two parameters. The discussion covers the relationship between compressibility factor, pressure, and temperature, and how to calculate the second virial coefficient. The professor also introduces the concept of fugacity and its relationship to ideal gas behavior. He emphasizes the importance of understanding ideal gas mixture properties as a starting point for more complex thermodynamic concepts. The class concludes with a brief mention of upcoming topics and a reminder for students to prepare questions for the next discussion session.