Gas Laws: Understanding Refrigeration's Core Principles

Refrigerators are heat engines that work in reverse, using coolants to transfer heat produced inside the refrigerator to the outside. This process is governed by several gas laws, including Gay-Lussac's Law, which states that the temperature of a gas is directly proportional to its pressure. Additionally, the F-Gas regulation aims to reduce and eventually ban the use of hydrofluorocarbons (HFCs) with high Global Warming Potential (GWP) by 2030, impacting the refrigeration industry. Understanding the gas laws is crucial for the effective design and operation of refrigeration systems, as they outline the behaviour of gases under various conditions of volume, pressure, temperature, and mass.

Gay-Lussac's Law

Mathematically, Gay-Lussac's Law can be expressed as:

P is the pressure exerted by the gas

T is the absolute temperature of the gas

The relationship between the pressure and absolute temperature of a given mass of gas at a constant volume can be illustrated graphically. The graph shows that as a gas is cooled at a constant volume, its pressure decreases constantly until the gas becomes a liquid through condensation.

Boyle's Law

P1 x V1 = P2 x V2

Where P1 and V1 are the initial pressure and volume, and P2 and V2 are the new pressure and volume.

Charles's Law

Jacques Charles, a French scientist, formulated Charles's Law, also known as the Law of Volumes, in the 18th century. This law is a fundamental principle in the thermodynamics of gases, establishing a direct relationship between the volume and temperature of a gas at constant pressure.

The law states that as temperature increases, the volume of a gas also increases, and when the temperature decreases, the volume of the gas decreases, provided that the pressure remains constant. This relationship can be expressed by the equation:

V1/T1 = V2/T2

Where:

• V1 is the initial volume of the gas
• T1 is the initial temperature in degrees Celsius (°C)
• V2 is the final volume of the gas
• T2 is the final temperature in degrees Celsius (°C)

Charles's interest in science was sparked by the birth of balloon aeronautics, specifically the first successful hot-air balloon launch in Paris in 1783. He later conducted his own balloon experiment, launching a hydrogen-filled balloon that achieved a much greater altitude. This led him to study gases, including hydrogen, oxygen, and carbon dioxide, and ultimately to the discovery of Charles's Law.

The First Law of Thermodynamics

Refrigerators are a common example of the application of gas laws in everyday life. They function as heat engines that work in reverse, transferring heat produced inside the refrigerator to the outside. This process involves the use of coolants, such as Freon, which undergo a cycle of expansion and compression.

Mathematically, this can be represented as:

\[\Delta \rm energy = + in - out\]

Or

\[\Delta E = E_2 - E_1 ={}_{1}Q_{2} - {}_{1}W_{2}\]

Where \(\Delta E\) represents the change in total energy, \(E_2\) and \(E_1\) are the final and initial states of the system, \({}_{1}Q_{2}\) is the heat added to the system, and \({}_{1}W_{2}\) is the work done by the system.

This law is crucial for understanding the refrigeration process. Refrigerators remove heat from their interior and transfer it to the outside, making the inside cooler. This process involves the use of coolants, which absorb heat from the inside and release it outside, in accordance with the First Law of Thermodynamics.

In addition to the First Law of Thermodynamics, refrigerators also utilise Gay-Lussac's Law and the heat of vaporisation of a liquid to remove heat from a system. Gay-Lussac's Law states that the temperature of a gas is directly proportional to its pressure when the volume is kept constant. This law, along with the First Law of Thermodynamics, helps explain the behaviour of gases within the refrigeration cycle.

The Ideal Gas Law

Refrigerators are essentially heat engines that work in reverse, transferring heat produced inside the refrigerator to outside the machine. This is achieved through a cycle of expansion and compression of a coolant, such as Freon, which absorbs heat from the air inside the refrigerator, creating a cooling effect.

The functioning of refrigerators is based on several gas laws, including Gay-Lussac's Law, which states that the temperature of a gas is directly proportional to its pressure. This law is applied in the pressurization of gases outside the refrigerator, leading to an increase in temperature. As the hot compressed gas flows through the coils, it heats up the condenser coils, and the subsequent decrease in pressure further cools the gas.

Another important law is Boyle's Pressure Law, which states that at a constant temperature, the volume of a gas is directly proportional to its pressure. This law describes the relationship between pressure and volume, with an increase in pressure resulting in a decrease in volume, assuming a constant temperature. This principle is fundamental to the compression and expansion of gases in the refrigeration cycle.

Charles' Law is also relevant, stating that at a constant pressure, the volume of a gas is directly proportional to its temperature. This law helps explain the behaviour of gases inside and outside the refrigerator, where changes in temperature lead to corresponding changes in volume.

\[ \dfrac{PV}{nRT}=1 \]

Here, $P$ represents pressure, $V$ is volume, $n$ is the number of moles of gas, $T$ is temperature, and $R$ is the gas constant. This equation describes the relationship between these variables and is applicable when the amount of gas is given and the mass remains constant.

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