Thermodynamics: Introduction and Basic Concepts Study Notes

1. Thermodynamics and Energy

• Thermodynamics is the science of energy and how it changes forms (like heat converting into mechanical motion).

• Energy is simply the ability to cause change.

• Conservation of Energy (First Law): Energy cannot be created or destroyed; it only changes form.

  • Balance equation: $\Delta E = E_{\text{in}} - E_{\text{out}}$

  • Example: A rock falling from a cliff starts with potential energy ($PE$) and turns it into kinetic energy ($KE$) as it falls, but total energy stays constant.

• Second Law of Thermodynamics: Energy has both quantity and quality. Natural processes only go in one direction, towards lower-quality energy.

  • Example: Hot coffee cools down in a cool room on its own; cold coffee never heats up by itself.

• Zeroth Law of Thermodynamics: If Object A is in thermal equilibrium with Object B, and B is in equilibrium with Object C, then A and C are also in equilibrium with each other. This is the basic principle behind thermometers.

• Two Approaches:

  • Classical Thermodynamics: Macroscopic view. Focuses on overall properties you can measure directly (like pressure and temperature) without worrying about individual atoms.

  • Statistical Thermodynamics: Microscopic view. Analyzes the average behavior of large groups of molecules.

2. Units and Dimensions

• Dimension: A physical characteristic (e.g., mass, length, time, temperature).

• Unit: The magnitude assigned to a dimension (e.g., kilogram, meter, second, kelvin).

• Primary vs. Secondary:

  • Primary (Fundamental): Base dimensions like mass ($m$), length ($L$), and time ($t$).

  • Secondary (Derived): Combinations of base dimensions, such as velocity ($\mathbf{V}$) or density ($\rho$).

• Force and Weight:

  • Force is governed by Newton's second law: $F = m a$.

  • In SI units: $1\,\text{N} = 1\,\text{kg}\cdot\text{m/s}^2$.

  • In English units: $1\,\text{lbf} = 32.174\,\text{lbm}\cdot\text{ft/s}^2$.

  • Weight ($W$): The force of gravity acting on mass: $W = m g$. Mass never changes, but weight depends on local gravity ($g \approx 9.81\,\text{m/s}^2$ on Earth).

• Energy vs. Power:

  • Energy: The amount of work or heat. Measured in joules ($1\,\text{J} = 1\,\text{N}\cdot\text{m}$), kilowatt-hours ($1\,\text{kWh} = 3600\,\text{kJ}$), or British thermal units ($1\,\text{Btu} = 1.0551\,\text{kJ}$).

  • Power: The rate at which energy is used or produced. Measured in watts ($1\,\text{W} = 1\,\text{J/s}$) or horsepower ($1\,\text{hp} = 746\,\text{W}$).

3. Systems and Control Volumes

• System: What you choose to study.

• Surroundings: Everything outside the chosen system.

• Boundary: The real or imaginary line dividing the system and surroundings.

• Types of Systems:

  • Closed System (Control Mass): Mass cannot enter or leave, but energy (heat and work) can cross the boundary. Example: Gas trapped in a sealed piston-cylinder.

  • Open System (Control Volume): Mass and energy can both flow across the boundary. Example: Water flowing through a pipe, turbine, or hair dryer.

  • Isolated System: Neither mass nor energy can cross the boundary.

4. Properties of a System

• Property: Any measurable characteristic of a system (e.g., pressure, temperature, volume).

  • Intensive Properties: Independent of system size. If you divide the system in half, these values stay the same (e.g., temperature $T$, pressure $P$, density $\rho$).

  • Extensive Properties: Depend on system size. If you divide the system in half, these values split in half (e.g., total mass $m$, total volume $V$, total energy $E$).

  • Specific Properties: Extensive properties per unit mass, turning them into intensive values (e.g., specific volume $v = \frac{V}{m}$).

• Continuum: The assumption that matter is continuous and evenly distributed rather than empty space with tiny molecules. Valid for all ordinary engineering problems.

5. Density and Specific Quantities

• Density ($\rho$): Mass per unit volume: $\rho = \frac{m}{V} \quad [\text{kg/m}^3]$

• Specific Volume ($v$): Volume per unit mass (reciprocal of density): $v = \frac{V}{m} = \frac{1}{\rho} \quad [\text{m}^3\text{/kg}]$

• Specific Gravity ($SG$): Density compared to pure water at $4^\circ\text{C}$ ($\rho_{\text{H}_2\text{O}} = 1000\,\text{kg/m}^3$): $SG = \frac{\rho}{\rho_{\text{H}_2\text{O}}}$

  • If $SG < 1$, the substance floats in water. If $SG > 1$, it sinks.

6. States, Equilibrium, and Processes

• State: The specific condition of a system, fixed by its properties.

• Thermodynamic Equilibrium: A state of complete balance:

  • Thermal: Equal temperature throughout.

  • Mechanical: No unbalanced pressures.

  • Phase: Mass of each phase stops changing.

  • Chemical: No ongoing chemical reactions.

• The State Postulate: To completely fix the state of a simple compressible system, you only need two independent, intensive properties (e.g., temperature and specific volume).

  • Note: During boiling or freezing, temperature and pressure depend on each other, so they cannot fix the state alone.

• Thermodynamic Processes:

  • Quasi-equilibrium Process: A process carried out slowly enough that the system remains practically in equilibrium at every step. This gives the theoretical maximum work output.

  • Isothermal: Temperature remains constant ($T = \text{constant}$).

  • Isobaric: Pressure remains constant ($P = \text{constant}$).

  • Isochoric (Isometric): Specific volume remains constant ($v = \text{constant}$).

  • Cycle: A series of processes that eventually returns the system back to its starting state.

  • Steady-Flow Process: Fluid flows through a control volume steadily, meaning conditions at any fixed point do not change with time.

7. Temperature Scales

• Thermodynamic (Absolute) Scales: Scales that start at absolute zero ($0\,\text{K}$ or $0\,\text{R}$), where molecular motion is minimized.

  • Kelvin ($\text{K}$) is the SI standard.

  • Rankine ($\text{R}$) is the English standard.

• Conversion Formulas:

  • $T(\text{K}) = T(^\circ\text{C}) + 273.15$

  • $T(\text{R}) = T(^\circ\text{F}) + 459.67$

  • $T(\text{R}) = 1.8 T(\text{K})$

  • $T(^\circ\text{F}) = 1.8 T(^\circ\text{C}) + 32$

• Temperature Differences ($\Delta T$):

  • A change of $1^\circ\text{C}$ is the exact same size as a change of $1\,\text{K}$: $\Delta T(\text{K}) = \Delta T(^\circ\text{C})$

  • A change of $1^\circ\text{F}$ equals a change of $1\,\text{R}$: $\Delta T(\text{R}) = \Delta T(^\circ\text{F}) = 1.8 \Delta T(\text{K})$

  • Rule of Thumb: Use absolute temperature ($\text{K}$ or $\text{R}$) for standalone temperatures in formulas; for temperature changes ($\Delta T$), $^\circ\text{C}$ and $\text{K}$ are interchangeable.

8. Pressure and Fluid Statics

• Pressure ($P$): Normal compressive force exerted per unit area: $P = \frac{F}{A} \quad [\text{Pa or N/m}^2]$

• Types of Pressure:

  • Absolute Pressure ($P_{\text{abs}}$): Measured relative to absolute vacuum ($0\,\text{Pa}$).

  • Gage Pressure ($P_{\text{gage}}$): Difference between absolute pressure and local atmospheric pressure: $P_{\text{gage}} = P_{\text{abs}} - P_{\text{atm}}$

  • Vacuum Pressure ($P_{\text{vac}}$): Pressure below atmospheric pressure: $P_{\text{vac}} = P_{\text{atm}} - P_{\text{abs}}$

• Pressure with Depth:

  • Pressure in a fluid increases with depth due to the weight of fluid above it: $P = P_{\text{atm}} + \rho g h$

  • Pressure does not change horizontally within the same static fluid.

  • Pascal's Principle: An applied pressure change transmits equally throughout an entire confined fluid, enabling hydraulic lifts: $\frac{F_1}{A_1} = \frac{F_2}{A_2}$

• Measurement Tools:

  • Barometer: Measures atmospheric pressure ($P_{\text{atm}} = \rho g h$).

  • Manometer: A U-tube fluid column used to find pressure differences. Add $\rho g h$ when moving downward in the tube; subtract $\rho g h$ when moving upward.

  • Bourdon Tube: A curved hollow metal tube that straightens under pressure to turn a dial needle.