08e59ee0-cf79-469b-803b-54cbb519443e.jpeg

# Thermodynamics ## Introduction - Thermodynamics is the study of energy, its transformations, and its relation to matter. - Thermodynamics is governed by a set of laws, which are based on experimental observations. ### Thermodynamic System - **System:** A quantity of matter or a region in space...

# Thermodynamics ## Introduction - Thermodynamics is the study of energy, its transformations, and its relation to matter. - Thermodynamics is governed by a set of laws, which are based on experimental observations. ### Thermodynamic System - **System:** A quantity of matter or a region in space chosen for study. - **Surroundings:** The mass or region outside the system. - **Boundary:** The real or imaginary surface that separates the system from its surroundings. ### Types of Systems 1. **Isolated System:** No exchange of mass or energy with the surroundings. 2. **Closed System:** Exchange of energy but not mass with the surroundings. 3. **Open System:** Exchange of both mass and energy with the surroundings. ### Properties of Systems - **Intensive Properties:** Do not depend on the size or extent of the system (e.g., temperature, pressure, density). - **Extensive Properties:** Depend on the size or extent of the system (e.g., mass, volume, energy). ### Thermodynamic Equilibrium - A system is in thermodynamic equilibrium if it maintains: - Thermal equilibrium (uniform temperature) - Mechanical equilibrium (uniform pressure) - Phase equilibrium (mass of each phase remains constant) - Chemical equilibrium (no change in chemical composition) ### Processes and Cycles - **Process:** Any change that a system undergoes from one equilibrium state to another. - **Path:** The series of states through which a system passes during a process. - **Cycle:** A process for which the initial and final states are identical. ### Types of Processes 1. **Isothermal Process:** Constant temperature. 2. **Isobaric Process:** Constant pressure. 3. **Isochoric (Isometric) Process:** Constant volume. 4. **Adiabatic Process:** No heat transfer. 5. **Isentropic Process:** Constant entropy. 6. **Throttling Process:** Constant enthalpy. ## Laws of Thermodynamics ### Zeroth Law - If two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. - This law allows us to define and measure temperature. ### First Law - The change in internal energy of a system is equal to the net heat added to the system minus the net work done by the system. - Mathematical Form: $\Delta U = Q - W$, where $\Delta U$ is the change in internal energy, $Q$ is the heat added to the system, and $W$ is the work done by the system. - The first law is a statement of the conservation of energy. ### Second Law - Heat cannot spontaneously flow from a colder body to a hotter body. - The entropy of an isolated system always increases or remains constant in a reversible process. - Mathematical Form: $\Delta S \geq 0$, where $\Delta S$ is the change in entropy. - The second law introduces the concept of entropy and the direction of thermodynamic processes. ### Third Law - The entropy of a perfect crystal at absolute zero temperature is zero. - Mathematical Form: $S \rightarrow 0$ as $T \rightarrow 0$ - This law provides a reference point for the determination of entropy. ## State Functions ### Important State Functions 1. **Internal Energy (U):** - Energy associated with the random, disordered motion of molecules. - A function of state, independent of the path. 2. **Enthalpy (H):** - Defined as $H = U + PV$, where $P$ is pressure and $V$ is volume. - Useful for analyzing processes at constant pressure. 3. **Entropy (S):** - A measure of the disorder or randomness of a system. - Related to the number of microstates available to the system. 4. **Gibbs Free Energy (G):** - Defined as $G = H - TS$, where $T$ is temperature. - Useful for determining the spontaneity of a process at constant temperature and pressure. ## Thermodynamic Relations ### Maxwell Relations - Derived from the fundamental thermodynamic relations. - Examples: - $(\frac{\partial T}{\partial V})_S = -(\frac{\partial P}{\partial S})_V$ - $(\frac{\partial T}{\partial P})_S = (\frac{\partial V}{\partial S})_P$ - $(\frac{\partial P}{\partial T})_V = (\frac{\partial S}{\partial V})_T$ - $(\frac{\partial V}{\partial T})_P = -(\frac{\partial S}{\partial P})_T$ ### Clapeyron Equation - Relates the change in pressure to the change in temperature during a phase transition. - Mathematical Form: $\frac{dP}{dT} = \frac{\Delta H}{T\Delta V}$, where $\Delta H$ is the enthalpy change and $\Delta V$ is the volume change during the phase transition. ## Applications ### Heat Engines - Devices that convert thermal energy into mechanical work. - Carnot Engine: A theoretical engine that operates on the Carnot cycle, providing the maximum possible efficiency. - Efficiency: $\eta = 1 - \frac{T_c}{T_h}$, where $T_c$ is the absolute temperature of the cold reservoir and $T_h$ is the absolute temperature of the hot reservoir. ### Refrigerators and Heat Pumps - Devices that transfer heat from a cold reservoir to a hot reservoir. - Coefficient of Performance (COP): - Refrigerator: $COP_R = \frac{Q_c}{W}$ - Heat Pump: $COP_{HP} = \frac{Q_h}{W}$ ### Phase Transitions - Processes involving the change from one state of matter to another (e.g., melting, boiling, sublimation). - Governed by the Clapeyron equation and phase diagrams. ### Chemical Reactions - Thermodynamics is essential for understanding the energy changes and equilibrium conditions in chemical reactions. - Gibbs free energy is used to predict the spontaneity of reactions. ## Conclusion - Thermodynamics provides a fundamental framework for understanding energy transformations and their relation to matter. - Its laws and principles are widely applied in various fields of science and engineering.