Charles’s Law is a foundational principle in the study of how gases behave, sometimes called the law of volumes. Named for the French physicist Jacques Charles, whose work in the 1780s detailed this predictable physical connection, the law describes a simple yet powerful interaction between two properties of a gas.
Defining the Direct Proportional Relationship
Charles’s Law states that for a fixed quantity of gas held at a constant pressure, the volume it occupies is directly proportional to its absolute temperature. This means that if the temperature of the gas increases, its volume will also increase proportionally. Conversely, a decrease in temperature will lead to a proportional decrease in volume.
For this relationship to hold true, two specific conditions must be maintained. The amount of gas must not change, meaning the system is closed and no gas is added or removed. The external pressure must also be held constant, allowing any change in temperature to be solely responsible for the resulting volume change.
The Absolute Temperature Requirement and Formula
Accurate application of Charles’s Law necessitates the use of the Kelvin scale, which is the absolute temperature scale. Kelvin is required because it begins at absolute zero, a theoretical point where all particle motion ceases. Since volume is directly tied to particle motion, the relationship must start from a true zero point, a condition that the Celsius or Fahrenheit scales do not meet.
The mathematical expression of the law is the proportionality \(V \propto T\), indicating that volume (\(V\)) is proportional to absolute temperature (\(T\)). This relationship can be converted into an equation by introducing a constant (\(k\)), resulting in the form \(V/T = k\). This shows that the ratio of a gas’s volume to its absolute temperature remains constant as long as the amount of gas and the pressure are unchanged.
When comparing a gas under two different sets of conditions, the practical comparison formula \(V_1/T_1 = V_2/T_2\) is often used. This equation allows scientists and engineers to predict the new volume (\(V_2\)) or to find a new temperature if the volume changes.
Underlying Kinetic Molecular Theory
The microscopic explanation for Charles’s Law is found in the Kinetic Molecular Theory (KMT) of gases. KMT posits that gas is composed of randomly moving particles whose average kinetic energy is directly related to the gas’s absolute temperature. When the temperature increases, the thermal energy causes the particles to move faster. This increased speed leads to a higher frequency of collisions with the container walls, and each collision exerts a greater force.
To maintain the constant external pressure defined by the law, the internal pressure generated by these faster particles must be balanced. The volume of the container must expand to counteract the increased force of the collisions. By expanding the volume, the particles have a greater distance to travel, which reduces the frequency of collisions per unit area. This expansion restores the balance with the external pressure, providing the mechanism for the observed volume increase.
Conversely, cooling the gas decreases the average kinetic energy of the particles, causing them to slow down. These slower particles hit the container walls less often and with less force, reducing the internal pressure. To keep the pressure constant, the container walls must contract, leading to a smaller volume.
Demonstrations of the Law in Action
The principle of Charles’s Law is readily observable in numerous everyday and industrial applications. The most dramatic example is the operation of a hot air balloon, where the air inside the envelope is heated by a burner. As the air temperature rises, the gas expands significantly, causing a large portion of the air mass to be expelled from the bottom of the balloon. This thermal expansion reduces the density of the air remaining inside, allowing the balloon to become buoyant and lift off the ground.
Another clear demonstration occurs when flexible containers, such as standard party balloons, are exposed to temperature extremes. A balloon placed outside on a very cold day will visibly shrink as the gas inside cools and contracts. The decreased temperature lowers the kinetic energy of the air molecules, which then require less volume to maintain the constant atmospheric pressure. When the same balloon is brought back into a warm room, the air molecules regain energy, push against the walls, and the volume quickly returns to its original size.
This relationship is also essential in the design of various systems, including weather balloons, which are launched into the upper atmosphere. As these balloons ascend, they encounter lower temperatures, which would cause the gas to contract, but they also experience significantly lower external atmospheric pressure, which allows the gas to expand. In controlled ground experiments, a gas in a sealed piston-cylinder assembly will see its volume double if its absolute temperature is successfully doubled, a predictable outcome of this fundamental gas law.