1 Thermodynamic Systems and Properties

Learn how thermodynamic systems are defined and classified, how equilibrium states are specified by properties, and how equations and units are used to describe them.

Define the system and its boundary

A is the matter or region selected for study. Everything outside it is the surroundings, and the boundary separates the two. The boundary can be a physical wall or an imagined surface, and it can be fixed or move; its choice determines what counts as crossing the system.

Classify systems and boundaries

Systems are classified by whether mass or energy can cross their boundaries:

A (control mass) does not allow mass to cross, but energy may cross. Gas sealed in a piston–cylinder is an example; the piston can move, changing the boundary and the system’s volume.
An (control volume) allows both mass and energy to cross. A turbine, pump, or filling tank can be analyzed this way.
An allows neither mass nor energy to cross. It is an idealization; a well-insulated, sealed container may approximate one.

Boundary descriptions also include how the boundary interacts with its surroundings. A rigid boundary does not move, whereas a movable boundary can. An adiabatic boundary prevents heat transfer, whereas a diathermal boundary permits it. These descriptions are independent: a rigid wall may still conduct heat.

Describe state and equilibrium

The state of a system is its condition as described by its properties. A is a property used to specify that condition; examples include pressure, temperature, volume, and composition. For a system in equilibrium, an appropriate independent set of state variables determines the other properties through relations such as an .

In , there are no unbalanced driving forces for change within the system. Thermal balance means there are no temperature differences driving heat transfer; mechanical balance means there are no unbalanced pressures or forces; and chemical and phase balance mean there is no net tendency for composition or phase to change. Introductory analysis often treats equilibrium states as uniform.

A system undergoing rapid change or containing strong gradients may not have a single well-defined equilibrium state, although local equilibrium approximations are sometimes useful. For a simple compressible substance, where pressure–volume effects are the only important mechanical effects, the state postulate says that two independent specify an equilibrium state.

Independence matters. In a pure substance that is a two-phase liquid–vapor mixture, saturation temperature and pressure are linked and do not independently identify the mixture’s state; another property, such as vapor quality, is needed.

Distinguish types of properties

A Property is a measurable characteristic of a system. depend on the amount of matter, while do not. For uniform material at the same condition, doubling the amount doubles extensive quantities.

Examples of are mass $m$ , total volume $V$ , and total internal energy $U$ . Examples of are temperature $T$ , pressure $p$ , and density $\rho$ .

are per unit mass and are therefore intensive. Specific volume and specific internal energy are defined by

v=\frac{V}{m}=\frac{1}{\rho},\qquad u=\frac{U}{m}.

Properties are determined by the state, not by the route taken to reach it. The change in a property between two states depends only on those states. Heat and work, by contrast, describe energy crossing a boundary during an interaction; they are not properties stored in a state.

Use equations and consistent units

An relates properties. For an ideal gas, the relation is

pV=mRT,

or, in specific form,

pv=RT,

where $R$ is the gas-specific constant. Under the ideal-gas model, pressure and absolute temperature determine specific volume for a known gas.

Use consistent units and check dimensions in every equation. Common SI units include mass in $\mathrm{kg}$ , length in $\mathrm{m}$ , time in $\mathrm{s}$ , temperature in $\mathrm{K}$ , pressure in $\mathrm{Pa}$ , volume in $\mathrm{m^3}$ , and energy in $\mathrm{J}$ . Specific energy is measured in $\mathrm{J/kg}$ , and density in $\mathrm{kg/m^3}$ . The kelvin is the SI unit of thermodynamic temperature.

Absolute temperature in kelvins is used in equations of state. Convert a Celsius temperature $t$ to an absolute temperature $T$ using

T\,[\mathrm K]=t\,[^\circ\mathrm C]+273.15.

For example, an ideal gas with $R=287\ \mathrm{J/(kg\cdot K)}$ , pressure $p=200\ \mathrm{kPa}$ , and temperature $T=300\ \mathrm K$ has specific volume

v=\frac{RT}{p}=\frac{287\times300}{200{,}000}=0.4305\ \mathrm{m^3/kg}.

If the system contains $0.50\ \mathrm{kg}$ , its volume is $V=mv=0.215\ \mathrm{m^3}$ . Pressure must be absolute when applying this gas relation.