Mathematical Relations , TdS equations and Clausius Clapeyron Equation
3 videos • 1,830 views • by Amit Mandal Hello viewers Dr. Amit Kr. Mandal here, Complete playlist of thermodynamics https://www.youtube.com/playlist?list... Mathematical Relations , TdS equations and Clausius Clapeyron Equation Thermodynamics is heavily reliant on mathematics to describe the behavior of systems and their interactions with their surroundings. This includes a variety of equations and relationships that connect different thermodynamic properties, such as: 1. State functions: Internal energy (U): Represents the total energy contained within a system, including its kinetic and potential energy. Enthalpy (H): Represents the sum of internal energy and the product of pressure and volume (PV). Entropy (S): Represents the measure of disorder or randomness within a system. Gibbs free energy (G): Represents the energy available to do work under constant temperature and pressure. Helmholtz free energy (A): Represents the energy available to do work under constant temperature and volume. These state functions are related to each other through various equations, such as: dH = dU + PdV: This equation defines enthalpy as the sum of internal energy and the product of pressure and volume change. dS = dQ/T: This equation defines entropy as the change in heat transfer (dQ) divided by the absolute temperature (T). dG = -SdT + VdP: This equation defines Gibbs free energy as a function of temperature, pressure, and entropy. 2. Maxwell relations: These are a set of four equations that relate the cross-derivatives of thermodynamic properties. They provide useful relationships between different state functions and are derived from the second law of thermodynamics. The Maxwell relations are: ∂S/∂V = ∂P/∂T ∂S/∂P = -∂V/∂T ∂H/∂T = Cp ∂G/∂T = -Sv where: Cp is the isobaric heat capacity. Cv is the isovolumetric heat capacity. 3. Equation of state: This is an equation that relates the pressure, volume, and temperature of a system. It can be specific to a particular substance or model a general behavior. Some common equations of state include: Ideal gas law: PV = nRT, where n is the number of moles of gas and R is the universal gas constant. van der Waals equation: (P + a/V^2)(V - b) = RT, where a and b are constants specific to the gas. 4. Other important equations: First law of thermodynamics: ΔU = Q - W, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. Second law of thermodynamics: It states that the entropy of an isolated system not in equilibrium tends to increase over time. These are just a few examples of the many mathematical relationships used in thermodynamics. Understanding these equations is essential for analyzing and predicting the behavior of thermodynamic systems in various applications. It is important to note that these equations are often accompanied by specific assumptions and limitations. It is crucial to understand the context and applicability of each equation for accurate analysis In this lucid lecture you will learn Learn about 1) Mathematical relations and maxwell equations in thermodynamics 2) Clausius Clapeyron equation 3) TDS equations