Thermodynamics Fundamentals

This cheat sheet covers fundamental concepts in thermodynamics, including energy, properties, processes, cycles, and the laws governing them. It provides definitions, formulas, and examples for understanding thermodynamic systems.

Core Principles

Energy can be converted from one form to another but cannot be created or destroyed (First Law).
The total entropy of an isolated system can only increase over time, or remain constant in ideal cases (Second Law).
Thermodynamic systems are defined by properties like pressure, temperature, volume, internal energy, enthalpy, and entropy.
Processes describe changes in a system's state, while cycles involve a series of processes returning the system to its initial state.
Ideal gas behavior is a simplification useful under specific conditions (low pressure, high temperature).
The compressibility factor (Z) accounts for deviations of real gases from ideal gas behavior.

Action Steps

Identify the system and its boundaries (open, closed, isolated).
Determine the initial and final states of the system using given properties.
Select appropriate thermodynamic tables or equations of state for property evaluation.
Apply the First and Second Laws of Thermodynamics to analyze energy and entropy changes.
Use process equations (e.g., isothermal, isobaric, adiabatic, polytropic) to relate state variables.
Calculate work and heat transfer based on the process and system type.

Formulas

Ideal Gas Law: $PV = mRT$ or $PV = n\bar{R}T$
Work (Simple Compressible System): $W = \int P dv$
First Law (Closed System): $dU = \delta Q - \delta W$
First Law (Open System, Steady State, Single Stream): $q - w = \Delta h + \Delta ke + \Delta pe$
Entropy Change (Ideal Gas): $ds = c_v \ln\frac{T_2}{T_1} + R \ln\frac{v_2}{v_1}$ or $ds = c_p \ln\frac{T_2}{T_1} - R \ln\frac{P_2}{P_1}$
Isentropic Process (Ideal Gas): $\frac{P_2}{P_1} = \left(\frac{v_1}{v_2}\right)^n = \left(\frac{T_2}{T_1}\right)^{\frac{n}{n-1}}$

Key Terms

System: A quantity of matter or a region in space chosen for study.
Surroundings: Everything outside the system.
State: The condition of a system described by its properties.
Process: A transformation from one state to another.
Cycle: A process or series of processes that return a system to its initial state.
Specific Volume (v): Volume per unit mass (inverse of density).
Enthalpy (h): A thermodynamic property defined as h = u + Pv.
Entropy (s): A thermodynamic property related to the disorder or randomness of a system.
Reversible Process: A process that can be reversed without leaving any change in the system or surroundings.
Irreversible Process: A process that cannot be reversed without leaving a change in the system or surroundings; always generates entropy.

Real World Examples

A power plant generating electricity.: Utilizes thermodynamic cycles (e.g., Rankine cycle) to convert thermal energy into mechanical work.
A refrigerator or air conditioner.: Uses thermodynamic principles (e.g., vapor-compression refrigeration cycle) to move heat from a low-temperature to a high-temperature reservoir.
An internal combustion engine.: Operates on cycles like the Otto or Diesel cycle to convert chemical energy into mechanical work.