Internal pressure

Gases have energy inside them.

This energy can change. It changes when a gas grows or shrinks.

Some gases are perfect. Their energy stays the same when they grow.

Other gases are real gases. Their energy changes when they move.

This can happen for two reasons. Tiny bits in the gas can pull. They can also push.

Scientists like James Joule studied this. He used metal tanks and water. He found that air can act like a perfect gas.

It is fun to learn how air works.

Gases hold energy inside them. Internal pressure is a way to measure this. It shows how energy changes when a gas grows or shrinks. This happens while the temperature stays the same.

Some gases are called perfect gases. In these gases, the tiny parts do not pull or push each other. Because of this, the energy stays the same when the gas expands.

Most gases are real gases. Their energy changes when they change size. This happens because of forces between the tiny parts. Sometimes the parts pull on each other. This makes the energy go up when the gas grows. Other times, the parts push away. This makes the energy go down when the gas grows.

James Joule studied this long ago. He moved air between two metal tanks. He used a water bath to keep the heat steady. He thought the internal pressure was zero. This made the air act like a perfect gas. Later, scientists measured carbon dioxide. They found its energy did change. This showed that real gases are not perfect.

Internal pressure is a way to measure energy. It shows how energy changes in a system. This happens when a system expands or shrinks. The temperature must stay the same during this change. Scientists use the symbol $\pi_T$ for this value. The unit used to measure it is the pascal. This idea helps us understand how gases behave.

How this works depends on the type of gas. In a perfect gas, the tiny parts do not interact. They have no potential energy between them. This means the energy does not change when the volume changes. The internal energy stays the same if the temperature is constant. Real gases are different because they have forces between their parts. These forces can pull or push the tiny particles.

Real gases show different results based on these forces. If parts pull on each other, the energy goes up. This happens when a gas expands. If the parts push away, the energy goes down. These forces are called attractive or repulsive forces. At a very large volume, these pressures reach zero. This makes a real gas act like a perfect gas.

Scientists have tested these ideas with real experiments. James Joule studied air in a famous expansion experiment. He moved high pressure air between two metal vessels. He used a water bath to keep the heat steady. Joule thought the internal pressure of air was zero. Later, Frederick Keyes and Francis Sears studied carbon dioxide. In 1925, they used better tools to measure it.

These tests help us see how gases work in the world. Keyes and Sears looked at carbon dioxide at 30 °C. They used pressures between 13.3 and 16.5 atm. They found the temperature dropped when pressure was lowered. This showed the internal pressure was negative. This discovery matched what the van der Waals equation predicted. It proves that real gases are not perfect.

Internal pressure is a specific way to measure energy changes in a system. It describes how internal energy shifts when a system expands or contracts. This process must happen at a constant temperature to be measured this way. Scientists use the symbol $\pi_T$ to represent this property. The standard unit for this measurement is the pascal. This value is important because it connects energy to the physical volume of a system. It is known as a thermodynamic equation of state. This means it links the state of a system to its energy properties.

To understand the mechanism, we look at how energy and volume interact. The internal pressure is defined as a partial derivative of internal energy with respect to volume. This calculation occurs while keeping the temperature constant. We can also express this value using temperature and pressure. The math involves the fundamental thermodynamic equation. By dividing this equation by volume at a constant temperature, we can find the internal pressure. We also use Maxwell relations to help solve these complex equations. These steps allow scientists to predict how energy will move within a system.

Different types of gases behave in very different ways. We can categorize them into perfect gases and real gases. In a perfect gas, the particles have no potential energy interactions. This means there are no forces pulling or pushing the particles together. Because of this, any change in internal energy is only linked to temperature. If the temperature stays constant, the internal energy does not change when volume changes. Therefore, the internal pressure of a perfect gas is zero. This is a very useful way to define what a perfect gas is.

Real gases are more complex because they have non-zero internal pressures. Their internal energy changes as they expand at a constant temperature. This happens because of the forces between the gas particles. If attractive forces are dominant, the internal energy increases during expansion. If repulsive forces are dominant, the internal energy decreases instead. As the volume becomes infinitely large, these internal pressures eventually reach zero. At this point, the real gas begins to act like a perfect gas.

We can use the van der Waals equation to model these real gases. This equation includes a specific parameter to account for molecular attraction. This parameter is always a positive value. Because of this, the internal pressure of a van der Waals gas is always positive. This means the internal energy of such a gas always increases during isothermal expansion. However, other real gases might show different results. Under specific temperatures and pressures, repulsive interactions might become more important. This could cause the internal pressure to change signs.

History shows us how scientists discovered these subtle energy shifts. James Joule conducted an expansion experiment to measure the internal pressure of air. He used an adiabatic process to pump air between two metal vessels. One vessel was evacuated to allow for expansion. The system sat in a water bath to keep the temperature steady. Joule observed no change in temperature during the experiment. He concluded that the internal pressure of air was zero. He believed the air acted as a perfect gas.

Later researchers found that Joule's results were not entirely complete. In 1925, Frederick Keyes and Francis Sears used better tools to study carbon dioxide. They performed measurements at 30 °C and pressures between 13.3 and 16.5 atm. They looked at the Joule coefficient, which is related to internal pressure. This coefficient can be measured by watching temperature changes during adiabatic free expansion. They found that the temperature dropped when the pressure was lowered. This showed that the internal pressure for carbon dioxide was negative. This discovery matched the predictions made by the van der Waals equation.