Comprehensive study notes: Thermodynamics - States, Processes, Temperature Scales, and Pressure

Thermodynamic states and process paths

A thermodynamic state is defined by two independent intensive quantities (e.g., pressure $p$ and temperature $T$) for a simple system; a state is a snapshot in time.
A process is the path the system follows between states; the same initial and final states can be connected by many different paths depending on how the process is executed.
In a piston-cylinder example, applying a force compresses the gas and causes $p$ and $V$ to change along the process path; the problem statement may specify how energy is exchanged with the surroundings (e.g., insulated, allowing or preventing heat transfer).
Problem qualifiers to watch for:
- Is the process insulated (adiabatic) or not?
- Is the process isentropic (constant entropy) or isenthalpic (constant enthalpy)? These terms tell you how to address the problem.
Types of processes mentioned (and distinctions):
- Isothermal: constant temperature $T$.
- Isenthalpic: constant enthalpy $H$.
- Isentropic: constant entropy $S$.
- Note: Isentropic and isenthalpic can sound similar when spoken quickly, but they are fundamentally different.
In complex systems (e.g., a car engine), the process is typically a sequence of multiple processes rather than a single simplified process.
A single process must start at an initial state and may have zero to $n$ intermediate states; the final state can return to the initial state (a cycle) or be a different state.
The path can be non-circular or even cross itself in the state space (P–V, T–S, etc.); the result depends on the path taken, not just the end states.

Steady vs unsteady processes

Steady processes: at any given snapshot in time, the system’s properties do not change with time; the same snapshot at a later time looks identical for the properties being considered.
In steady-state analysis, you analyze the system as if time is not changing.
Unsteady processes: time-dependence is important. Chapter 5 will cover unsteady analysis (e.g., filling a gas tank, transient flows).

Thermal equilibrium and heat transfer

Thermal equilibrium means two bodies (or regions) are at the same temperature and there is no net heat transfer between them.
The Zeroth Law of Thermodynamics: if A is in thermal equilibrium with B, and B is in thermal equilibrium with C, then A is in thermal equilibrium with C.
Everyday example: iced coffee warming to room temperature; hot coffee cooling toward room temperature; two bodies reach the same temperature when in contact.
Heat transfer drives energy flow from higher to lower energy states (hot to cold) until equilibrium is reached.
Temperature scales discussed: Celsius (°C) and Fahrenheit (°F) are non-absolute scales; their zero points are not absolute and depend on reference points (e.g., freezing point of water for °C).
Absolute scales (required for thermodynamics): Kelvin (K) or Rankine (°R). These scales have an absolute zero where molecular motion ceases.
Why absolute scales matter: many equations use temperature in the denominator or as an absolute quantity; using a non-absolute scale can lead to undefined or nonsensical results at zero.
Common thermodynamics practice: convert problems to an absolute temperature scale (usually Kelvin) whenever temperatures appear in equations.
Origin of absolute zero (historical note): experiments in the 19th century with various gases led to extrapolation to a lowest possible temperature, approximately $-273.15^\circ C$, where atomic motion ceases; this defines absolute zero.
Temperature change equivalence: a change of $10$ K is the same magnitude as a change of $10^\circ C$ (for temperature differences, not the absolute values).
Quick aside on notation: the lecturer mentions Rankine (often written as Rankine or °R) as the absolute-Fahrenheit-based scale; Kelvin is the SI absolute scale used in most engineering contexts. Convert to Kelvin when problems use Celsius or Fahrenheit.
Important takeaway: use absolute temperatures in analyses involving temperatures in denominators or in state functions.

Temperature scales and absolute zero

Non-absolute scales: Celsius, Fahrenheit; zero points tied to specific physical references (water freezing, etc.).
Absolute scales: Kelvin (K) and Rankine (°R).
Conversion relationships (for reference):
- T{ ext{K}} = T{ ext{C}} + 273.15
- T{ ext{R}} = T{ ext{F}} + 459.67 (less commonly used in this course; Kelvin is standard for SI)
Absolute zero: T_0 = 0 ext{ K} ext{ (equivalently } -273.15^ ext{C})
Change equivalence: for a change in temperature, riangle T{ ext{K}} = riangle T{ ext{C}}; i.e., a $10$ K change equals a $10^ ext{C}$ change.

Pressure units and concepts

Pressure units commonly used in engineering:
- Pascal (Pa): 1 ext{ Pa} = 1rac{ ext{N}}{ ext{m}^2}
- Bar: 1 ext{ bar} = 10^5 ext{ Pa} = 0.1 ext{ MPa}
- Kilopascal (kPa): 1 ext{ kPa} = 10^3 ext{ Pa}
- Atmosphere (atm): 1 ext{ atm} \, ext{(approximately)} \, 101{,}325 ext{ Pa}
In practice, gauges measure gauge pressure (pressure relative to atmospheric pressure). Absolute pressure is gauge pressure plus atmospheric pressure:
- p{ ext{abs}} = p{ ext{gauge}} + p_{ ext{atm}}
- p{ ext{gauge}} = p{ ext{abs}} - p_{ ext{atm}}
Atmospheric pressure context: we live with atmospheric pressure around us; a tire gauge, for example, reads gauge pressure, not absolute pressure unless specified.
Vacuum pressure concept: how far below atmospheric the pressure is (usually described as a negative gauge pressure relative to atmosphere).

Hydrostatic pressure and the role of depth

Hydrostatic pressure in a static fluid under gravity:
- At a given depth, the pressure increases with depth: p = p_{ ext{atm}} +
  ho g h where $
  ho$ is fluid density, $g$ is gravitational acceleration, and $h$ is the vertical depth from the surface.
Key properties:
- Pressure in the same fluid at the same depth is the same, regardless of the container shape (Pascal’s principle in fluids).
- Pressure acts perpendicular to the surfaces of the container (normal to the surface).
Densities matter: mercury is ~$13{,}600 ext{ kg/m}^3$; water is ~$1000 ext{ kg/m}^3$; thus, deeper columns with mercury create much larger pressure changes than water for the same height increment.
Conceptual visualization: a balloon with internal pressure balanced by external atmospheric pressure; inner pressure is transmitted equally in all directions (spherical symmetry) and balanced by the outside pressure.

Pascal's law and hydraulic systems

Pascal’s law (hydraulic principle): pressure transmitted undiminished in an enclosed incompressible fluid.
For two pistons with areas $A1$ and $A2$ connected by fluid:p1 = p2 \ F1/A1 = F2/A2
Mechanical advantage:rac{F2}{F1} = rac{A2}{A1}
Practical example: hydraulic jack—small force on a small piston yields a large force on a larger piston, enabling lifting of heavy loads.

Manometers and pressure measurement

Manometer as an analog method to measure pressure differences using a height column of a liquid.
Concept:
- Two fluids of different densities are connected; the height difference encodes the pressure difference between the two sides.
- If the interface heights are equal, the pressures at that interface in the two media are equal (static equilibrium).
Example usage: wind tunnel measurements, gas cylinders, or laboratory setups involving two fluids (one often mercury, the other another liquid such as water or oil).
Relation to absolute vs gauge: the height column provides a measure that reflects the pressure difference; adding atmospheric pressure yields absolute pressure when needed.
Real-world note: historical aerodynamic studies relied on manometers; modern labs still illustrate the principle, even if not always used in flight test facilities today.

Multi-fluid stratification and total pressure at depth

When multiple fluids stack due to density differences, the total pressure at a depth is the sum of the contributions from each fluid plus the atmospheric pressure at the surface:
- Absolute pressure at depth in a stratified column:
- $$p{ ext{abs}} = p{ ext{atm}} +
  ho1 g h1 +
  ho2 g h2 +
  ho3 g h3 + \