Basic gas concepts for understanding Carbon Dioxide Removal (CDR): Gases can be described by their state which is dependent on their pressure, volume, and temperature.

Summary

Understanding gas behavior is crucial for analyzing energy requirements in carbon capture systems. Gases are characterized by compressibility, low density, and no fixed shape, with their state defined by pressure, volume, and temperature relationships. State changes through compression/expansion or phase transitions involve significant energy exchanges due to molecular motion and thermodynamic principles. Capturing CO₂ from air requires overcoming entropy-driven dispersion and enthalpy changes, with theoretical minimum energy requirements determined by Gibbs free energy.

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In order to understand why Direct Air Capture (DAC) systems are so energy intensive and why there is a theoretical minimum energy requirement for capturing carbon dioxide, it is important to understand some basic gas concepts.

What is a gas?

Gases are one of the fundamental states of matter which also include solids, liquids, plasma, as well as various intermediate states. Gases can be categorized by:

• High compressibility: Gases can be compressed into smaller volumes.
• Low density: Gas particles are widely spaced compared to liquids or solids.
• No fixed shape or volume: Gases expand to fill their container.

Essentially, gases are particles that can move around freely and randomly, leading to continuous collisions with each other and the walls of their container, creating pressure.

The state of a gas

Gases are often described as being in a 'state' which is described by its known properties. The state of a gas is described by its pressure (P), volume (V), and temperature (T), governed by the ideal gas law:

$$\begin{align*} \text{PV} &= \text{nRT} \\ \end{align*}$$

Where:

• P: is the pressure of the gas
• V: is the volume of the gas
• n: is the number of moles of gas
• R: is the ideal gas constant
• T: is the temperature of the gas in Kelvin

Key Concepts:

• Pressure: The force exerted by gas particles colliding with surfaces.
• Volume: The space occupied by the gas; compressing or expanding the gas changes its pressure and temperature.
• Temperature: Related to the average kinetic energy of gas particles; higher temperatures mean faster-moving particles.

State Changes in Gases

Gases can change their state through processes that involve energy transfer. These include:

1. Compression and Expansion:

• Compression: Reducing the gas's volume increases its pressure and temperature. This can be observed when compressing a sealed container such as when you pump up a bike tire and it becomes harder to pump. As the volume of the gas in the tire cannot readily change, the pressure and temperature of the air in the tire increases.
• Expansion: Increasing the volume decreases pressure and temperature. This can be observed when a pressurized gas is rapidly released from a container and it feels cold to the touch, as is the case when using spray-on deodorant.
• Energy is required or released due to work done on or by the gas. When you compress a gas, you have to do work on the gas to overcome the force of the gas particles colliding with the walls of the container. When a gas expands, it often feels cold to the touch because the gas uses its energy to push against its surroundings during the expansion. This reduces the energy available for the motion of the gas particles, lowering their temperature and making it feel cold.

2. Phase Changes:

• Gases can change to other states (e.g., liquid or solid) through condensation or deposition. These processes involve overcoming or harnessing intermolecular forces.
• Latent heat: The energy absorbed or released during phase changes without a change in temperature.

Why State Changes Involve Energy

Molecular Motion In a gas, molecules move freely. Changing a gas's state often requires adjusting molecular energy:

• Increasing energy (e.g., heating) to overcome intermolecular attractions when transitioning from liquid to gas
• Reducing energy (e.g., cooling) to condense a gas into liquid or solid

Work and Heat

• Compressing a gas (e.g., for carbon storage) requires work, adding energy to the system.
• Expanding a gas allows it to perform work, releasing energy.

Phase Change Energy

• Condensing a gas into a liquid involves releasing the energy of vaporization, as molecules lose enough kinetic energy to stick together.

Enthalpy and Entropy

Enthalpy and entropy are thermodynamic properties that describe the energy and disorder of a system which relate to the state changes of gases. Enthalpy and entropy can be confusing concepts to understand, but what needs to be known is:

• Enthalpy: Relates to the heat content of a system. When a gas is compressed or cooled, its enthalpy decreases as it loses energy, often as heat.
• Entropy: Relates to the number of ways particles in a system can be arranged. Gases naturally expand to fill available space because doing so increases entropy, making the system more thermodynamically stable. For example, if unpressurized carbon dioxide is released into a sealed room, the gas will spread throughout the room over time, as the constant motion of the particles causes them to distribute evenly, maximizing entropy.

The energy required for state changes in gases depends on two factors: how much heat is absorbed or released (enthalpy) and how much disorder changes (entropy).

Conclusion

The thermodynamic analysis of gases is a complex topic that has been simplified in this section. In the context of carbon capture and DAC, the key takeaway is that gases can be described by their state (e.g., concentration, pressure, and temperature), and that changing the state or concentration of a gas involves energy. DAC involves extracting carbon dioxide from a low concentration in the air and concentrating it in a captured form. Using thermodynamic principles, it is possible to calculate the minimum energy required for this process using a property called Gibbs free energy, which defines the theoretical lower bound for this state change.