1.3 Properties, state, and equilibrium

Properties, State, and Equilibrium

Properties, state, and equilibrium are the building blocks you'll use throughout thermodynamics. Every analysis of an energy system starts by defining what state a system is in, what properties describe it, and whether it's in equilibrium. Getting these concepts down now makes everything that follows much easier.

Extensive vs. Intensive Properties

Defining Extensive and Intensive Properties

Extensive properties depend on the size (or extent) of a system. If you double the amount of material, you double the property's value. Volume, mass, total energy, and entropy are all extensive.

Intensive properties don't depend on system size. Temperature, pressure, and density stay the same whether you're looking at a small sample or the whole system.

A quick test: imagine splitting a system into two equal halves. If the property value halves, it's extensive. If it stays the same, it's intensive.

Relationships Between Extensive and Intensive Properties

• Dividing an extensive property by mass gives a specific property, which is intensive. For example, specific volume $v = \frac{V}{m}$ has units of $\text{m}^3/\text{kg}$ and doesn't depend on system size.
• More generally, the ratio of two extensive properties is always intensive. Density $\rho = \frac{m}{V}$ is a classic example.
• Extensive properties are additive across subsystems. If a tank is divided into two compartments with volumes $V_1$ and $V_2$, the total volume is $V_1 + V_2$.
• Intensive properties are not additive. If one compartment is at 300 K and the other is at 400 K, the system temperature is not 700 K.

Thermodynamic State and Variables

Understanding Thermodynamic State

The thermodynamic state of a system is its condition as described by a set of properties at a given instant. Think of it as a snapshot: if you know the right properties, you know everything about the system at that moment.

A state variable (or state property) depends only on the current state, not on how the system got there. Common state variables include:

• Pressure ($P$)
• Temperature ($T$)
• Volume ($V$)
• Internal energy ($U$)
• Enthalpy ($H$)
• Entropy ($S$)

This "path independence" is what makes state variables so useful. Whether a gas was heated slowly or compressed rapidly to reach 500 K and 200 kPa, its internal energy at that state is the same.

Thermodynamic Processes and the State Postulate

A thermodynamic process is a change from one equilibrium state to another. You describe a process by its initial state, final state, and the path connecting them. Some common idealized processes:

• Isothermal: constant temperature
• Isobaric: constant pressure
• Isochoric (isometric): constant volume
• Adiabatic: no heat transfer across the boundary

The state postulate tells you how many independent properties you need to fully define a state. For a simple compressible system (one where effects like motion, gravity, electricity, and magnetism are negligible), the state is fixed by specifying two independent, intensive properties.

"Independent" is the key word here. During a phase change, temperature and pressure are not independent of each other (they're locked together by the saturation curve), so you'd need a different pair, like pressure and specific volume.

Thermodynamic Equilibrium and Types

Defining Thermodynamic Equilibrium

A system is in thermodynamic equilibrium when there are no unbalanced driving forces anywhere within it. In practical terms, none of its macroscopic properties are changing with time, and there's no tendency for change.

For full thermodynamic equilibrium, a system must satisfy all three types of equilibrium simultaneously:

Types of Thermodynamic Equilibrium

• Thermal equilibrium: Temperature is uniform throughout the system. No net heat transfer occurs within the system or between the system and its surroundings. A cup of coffee sitting in a room will eventually reach the room's temperature; at that point, the coffee and the room air are in thermal equilibrium.
• Mechanical equilibrium: Pressure is uniform throughout the system (ignoring gravity effects) and doesn't change with time. There are no unbalanced forces. A gas in a rigid, sealed container at rest is in mechanical equilibrium.
• Chemical equilibrium: The chemical composition doesn't change with time. For reacting systems, forward and reverse reactions proceed at equal rates, so there's no net change in the amounts of reactants or products. A saturated salt solution where the rate of dissolution equals the rate of crystallization is one example.

A system can satisfy one type of equilibrium without satisfying the others. For instance, a gas at uniform temperature (thermal equilibrium) could still have a pressure gradient (not in mechanical equilibrium).

State Postulate for Simple Systems

Applying the State Postulate

For a simple compressible system, two independent, intensive properties completely fix the state. Once those two are specified, every other intensive property is determined.

Common pairs used in practice:

• Temperature and specific volume ($T, v$)
• Pressure and specific enthalpy ($P, h$)
• Pressure and specific entropy ($P, s$)

Once you fix the state with two properties, you can find any other property using equations of state, property tables, or software. For example, if you know $T$ and $v$ for an ideal gas, you can find pressure from the ideal gas law:

$Pv = RT$

where $R$ is the specific gas constant for that substance.

Property Relations and Diagrams

The state postulate is what makes property tables and diagrams possible. Since two independent properties fix the state, you can map all the other properties onto two-dimensional diagrams:

• P-v diagram: Plots pressure vs. specific volume. The area under a process curve on this diagram represents boundary work per unit mass.
• T-s diagram: Plots temperature vs. specific entropy. The area under a process curve here represents heat transfer per unit mass.
• P-v-T surface: A 3D surface showing how pressure, specific volume, and temperature relate for a given substance, including phase-change regions.

These diagrams are not just visual aids. You'll use them constantly to sketch processes, identify states, and check whether your calculations make sense. Getting comfortable reading them now will pay off throughout the course.