Introduction to Thermodynamics
3. State Variables
Learning outcomes
- I can identify pressure, volume, temperature, and internal energy as state variables.
- I can distinguish between state variables and process variables.
- I can explain how state variables describe a system.
- I can predict how changing one variable affects another.
- I can interpret simple thermodynamic state diagrams.
Introduction
To understand a thermodynamic system, scientists must be able to describe its condition at any moment. Instead of tracking every individual particle, they use a small set of measurable quantities called state variables. These variables describe the overall condition, or state, of a system.
For example, if you know the pressure, volume, and temperature of the air inside a bicycle tyre, you have a good description of its thermodynamic state. If any of these quantities changes, the state of the system changes as well. State variables help scientists predict how systems behave and form the basis of many important gas laws and thermodynamic equations.
What Are State Variables?
A state variable is a measurable property that describes the current condition (state) of a thermodynamic system.
State variables describe the system itself, not how it reached that state.
Common state variables include:
- Pressure (P)
- Volume (V)
- Temperature (T)
- Internal energy (U)
Knowing these variables allows scientists to describe the condition of a system.
Figure 1. State variables describe the condition of a thermodynamic system.
Pressure
Pressure (P) is the force exerted per unit area.
In gases, pressure is caused by particles colliding with the walls of their container.
Pressure depends on factors such as:
- Temperature.
- Volume.
- Number of gas particles.
Common units include:
- Pascal (Pa)
- Kilopascal (kPa)
- Atmosphere (atm)
Higher pressure means particles collide with the container walls more frequently or more forcefully.
Volume
Volume (V) is the amount of space occupied by a substance.
For gases:
- Volume usually refers to the size of the container holding the gas.
Common units include:
- Cubic metre (m³)
- Cubic centimetre (cm³)
- Litre (L)
Changing the volume often changes the pressure and temperature of a gas.
Temperature
Temperature (T) measures the average kinetic energy of the particles in a substance.
Higher temperature means:
- Faster-moving particles.
- More energetic collisions.
The SI unit of temperature is the kelvin (K).
Degrees Celsius (°C) are also commonly used.
Internal Energy
Internal energy (U) is the total microscopic energy stored within a substance.
It includes:
- The kinetic energy of moving particles.
- The potential energy due to forces between particles.
Internal energy changes when:
- Heat is transferred.
- Work is done on or by the system.
Internal energy is another important state variable.
Figure 2. Pressure, volume, temperature, and internal energy are all linked through the behaviour of particles.
State Variables vs Process Variables
State variables and process variables describe different aspects of thermodynamics.
State Variables
Describe the condition of the system.
Examples:
- Pressure
- Volume
- Temperature
- Internal energy
Their values depend only on the current state.
Process Variables
Describe how energy is transferred during a change.
Examples:
- Heat (Q)
- Work (W)
Process variables depend on the path taken between two states, not just the starting and ending conditions.
Comparing State and Process Variables
| State Variables. | Process Variables |
|---|---|
| Pressure | Heat |
| Volume | Work |
| Temperature | |
| Internal energy |
State variables describe the system.
Process variables describe changes occurring to the system.
How State Variables Describe a System
Suppose a sealed gas container has:
- Pressure = 200 kPa
- Volume = 2.0 L
- Temperature = 300 K
These values completely describe the current state of the gas.
If the gas is heated:
- Temperature increases.
- Pressure may increase.
- Internal energy increases.
The system has entered a new thermodynamic state.
Figure 3. Changing one state variable often changes the others, resulting in a new thermodynamic state.
Relationships Between State Variables
The state variables are often connected.
Examples include:
Increase Temperature
If volume remains constant:
- Pressure increases.
Increase Volume
If temperature remains constant:
- Pressure decreases.
Compress a Gas
- Volume decreases.
- Pressure increases.
- Internal energy may increase if the gas is compressed rapidly.
These relationships are explained by the kinetic particle model and later by the gas laws.
Predicting Changes
Understanding state variables allows us to predict what happens when conditions change.
| Change | Likely Effect |
|---|---|
| Heat a sealed gas. | Pressure increases |
| Compress a gas | Pressure increases |
| Expand a gas | Pressure decreases |
| Cool a gas | Pressure decreases |
These predictions are based on particle behaviour.
State Diagrams
A state diagram is a graph showing how one state variable changes with another.
Common examples include:
- Pressure–Volume (P–V) diagrams.
- Pressure–Temperature (P–T) diagrams.
- Volume–Temperature (V–T) diagrams.
Each point on a state diagram represents one particular state of the system.
Moving from one point to another represents a thermodynamic process.
Figure 4. A pressure–volume (P–V) diagram shows how the state of a system changes during a thermodynamic process.
Reading a Simple State Diagram
Consider a simple Pressure–Volume (P–V) graph.
If the graph moves:
- Upwards → Pressure increases.
- Downwards → Pressure decreases.
- Right → Volume increases.
- Left → Volume decreases.
Each point represents a different state.
The path between points shows how the system changed.
Later in thermodynamics, these diagrams will be used to calculate work done by gases.
Why State Variables Matter
State variables allow scientists and engineers to:
- Describe systems accurately.
- Predict system behaviour.
- Analyse engines.
- Study gases.
- Design refrigeration systems.
- Improve energy efficiency.
They are fundamental to every area of thermodynamics.
Figure 5. State variables are used to analyse engines, refrigerators, power plants, and many other thermodynamic systems.
Worked Example
Question
A sealed container of gas is heated while its volume remains constant.
Predict what happens to:
- Temperature
- Pressure
- Internal energy
Solution
- Temperature increases because the particles move faster.
- Pressure increases because faster-moving particles collide more frequently and with greater force against the container walls.
- Internal energy increases because the particles have more kinetic energy.
Real-World Connection
A pressure cooker is a practical example of changing state variables. As the cooker is heated, the temperature of the water and steam increases. Because the lid is sealed, the volume remains almost constant, causing the pressure inside the cooker to rise. The higher pressure allows water to boil at a higher temperature, helping food cook more quickly.
Did You Know?
Meteorologists measure atmospheric pressure, temperature, and sometimes humidity at thousands of locations around the world every day. These measurements describe the state of the atmosphere and are used by computer models to predict weather patterns and storms.
Key Terms
Internal energy (U) – The total microscopic energy stored within a substance.
Pressure (P) – The force exerted per unit area by particles colliding with a surface.
Process variable – A quantity, such as heat or work, that describes energy transferred during a process.
State – The current condition of a thermodynamic system.
State diagram – A graph showing the relationship between state variables during a thermodynamic process.
State variable – A measurable property that describes the current condition of a thermodynamic system.
Temperature (T) – A measure of the average kinetic energy of the particles in a substance.
Volume (V) – The amount of space occupied by a substance.
Key Takeaways
- Pressure, volume, temperature, and internal energy are important state variables that describe the condition of a thermodynamic system.
- State variables describe the current state of a system, while process variables such as heat and work describe energy transfers during changes.
- Changing one state variable often affects the others because they are interconnected.
- State variables allow scientists to predict how thermodynamic systems behave under different conditions.
- State diagrams, such as pressure–volume (P–V) graphs, visually represent changes in the state of a system.
- Understanding state variables provides the foundation for studying gas laws, heat engines, and many other topics in thermodynamics.