BE1610 Thermodynamics Study Notes

Overview and History of Thermodynamics

Thermodynamics is the study of the fundamental relationships between heat, work, temperature, and energy, based on the principle that heat is a form of energy convertible into mechanical work. Derived from the Greek words thermo (heat) and dynamics (movement), the field was formalized in the 19th century to optimize steam engine efficiency during the Industrial Revolution. Key figures like Sadi Carnot and Lord Kelvin helped transition the study from empirical observations to a rigorous science. Modern thermodynamics focuses on macroscopic scales and equilibrium states, providing the framework for analyzing power plants, chemical process energy requirements, and refrigeration cycles.

Laws of Thermodynamics

1. 0th Law of Thermodynamics (Thermal Equilibrium): This law serves as the basis for temperature measurement. It states that if two systems ($A$ and $C$) are each in thermal equilibrium with a third system ($B$), then $A$ and $C$ are in thermal equilibrium with each other. This implies they share a common property: temperature (𝑇𝐴𝐴 = 𝑇𝑇𝐶𝐶 = 𝑇𝑇𝐶𝐶 = 𝑇𝑇𝐵).

2. 1st Law of Thermodynamics (Conservation of Energy): Energy can neither be created nor destroyed, only transformed. For a closed system, the change in internal energy ($\Delta U$) equals the heat added to the system ($Q$) minus the work done by the system ($W$):
   $\Delta U = Q - W$

3. 2nd Law of Thermodynamics (Entropy): This law defines the direction of energy flow. It states that for any spontaneous process, the total entropy ($S$) of an isolated system always increases ($\Delta S \geq 0$), signifying that energy quality degrades as it is transferred.

Definitions and Properties of Systems

Thermodynamics utilizes specific definitions to analyze energy changes within boundaries:

• Systems:

  • Open Systems: Both mass and energy can cross the boundaries (e.g., a turbine or pump).

  • Closed Systems: No mass transfer occurs, but energy transfer is possible (e.g., a piston-cylinder).

  • Isolated Systems: Neither mass nor energy can cross the boundaries (e.g., a perfectly insulated vacuum flask).

• Properties:

  • Intensive Properties: Independent of the amount of substance (e.g., Temperature $T$, Pressure $P$, density $\rho$).

  • Extensive Properties: Proportional to the system's mass (e.g., total volume $V$, total mass $m$).

  • Specific/Molar Units: Extensive properties converted to intensive values by dividing by mass or moles (e.g., specific volume $v = V/m$).

• Process Types:

  • Isobaric: Constant pressure ($\Delta P = 0$).

  • Isometric/Isochoric: Constant volume ($\Delta V = 0$).

  • Isothermal: Constant temperature ($\Delta T = 0$).

  • Adiabatic: No heat transfer between system and surroundings ($Q = 0$).

Thermodynamic Functions and State Equations

• Internal Energy ($U$): A state function representing the microscopic kinetic and potential energy of molecules.

• Enthalpy ($H$): Total heat content, defined as $H = U + PV$. In constant-pressure processes, the change in enthalpy often equals the heat flow ($\Delta H = Q_p$).

• Heat Capacities: Defined as $C<em>p$ (constant pressure) and $C</em>v$ (constant volume), representing the energy needed to increase temperature.

• Gibbs Phase Rule: Determines the degrees of freedom ($F$) required to define a system's state: $F = C - P + 2$, where $C$ is the number of components and $P$ is the number of phases.

• State vs. Path Functions: State functions (e.g., $P, V, T, U$) depend only on the current equilibrium state; path functions (e.g., $Q, W$) depend on the transition process used to reach that state.

Units, Dimensions, and Consistency

• Standard Dimensions (SI): Mass (kg), Length (m), Time (s), Temperature (K), and Amount (mol).

• Molar Mass ($M$): Relationship between mass and moles ($m = n \times M$). Examples include $O<em>2 = 32 \text{ g/mol}$ and $CO</em>2 = 44 \text{ g/mol}$.

• Dimensional Homogeneity: Every term in an equation must have identical units. This allows for the derivation of Dimensionless Groups used in scaling.

• Example: The Sherwood number ($S_{Sh} = \frac{hD}{L}$) is a dimensionless group used to characterize mass transfer, where $h$ is the mass transfer coefficient, $D$ is the diffusion coefficient, and $L$ is the characteristic length.