Charles’ law states that, at constant volume, the pressure of a gas increases proportionally to its temperature. This means that if the temperature of a gas is increased,** its pressure will also increase in proportion. **Therefore, it can be said that Charles’s law relates the acceleration of temperature to the pressure of the gas.

## What is Charles Gay Lussac’s law?

Charles Gay-Lussac’s law, also known as Gay-Lussac’s law, is a gas law that establishes a direct relationship between the temperature and pressure of a gas at constant volume. This law **was formulated by two French scientists, **Joseph Louis Gay-Lussac and Jacques Charles, in the first half of the 19th century.

Gay-Lussac’s law, on the other hand, states that at constant pressure, the volume of a gas is proportional to its temperature. That is, if the temperature of a gas at constant pressure is increased, its volume will also increase in proportion. The ideal gas law combines both laws, along with the Boyle-Mariotte law, to establish a relationship between pressure, volume, temperature, and quantity of gas. The physical constant used in this law is the **ideal gas constant, symbolized as R.**

Some examples of application of Charles Gay-Lussac’s law include the behavior of gases in the atmosphere and in cooking. For example, when baking ‘*cookies*‘, the air inside the oven gets hot, which **increases** **the pressure of the gas inside.** This causes the cookies to expand and cook evenly.

Another important concept related to the gas law is density. The density of a gas refers to the amount of mass found in a unit volume. As mentioned above, Charles’s law states that, **At constant volume, the pressure of a gas increases** proportionally to its temperature. This means that, at constant temperature, if the pressure of a gas is increased, its density will also increase proportionally.

## What is the constant in Gay Lussac’s law?

The constant used in Gay-Lussac’s law is the constant of ratio between the pressure and the temperature of a gas at constant volume. This constant is represented by the letter k and is used to express the **mathematical relationship between pressure and temperature** of a gas in units of absolute pressure and temperature.

The constant k can be calculated using the ideal gas equation of state, which relates the pressure, volume, temperature, and amount of gas. This equation states that the pressure of a gas **is equal to the ideal gas constant, **multiplied by the absolute temperature, and divided by the volume. Therefore, the constant k can be obtained by dividing the pressure by the absolute temperature at constant volume.

The constant k is also known as Charles’s law. This name comes from Jacques Charles, who was the first to investigate the relationship between the **temperature and** **the volume of a gas at constant pressure**. Charles discovered that at constant pressure, the volume of a gas decreases in proportion to the decrease in temperature. This is known as Charles’s law, which establishes the relationship between the volume and the temperature of a gas at constant pressure.

## What is Gay Lussac’s second law?

Unlike Gay-Lussac’s first law, which refers to the relationship between temperature and pressure of a gas at constant volume, Gay-Lussac’s second law refers to the relationship between temperature and volume of a gas. gas at constant pressure. This law states that, at constant pressure, **The volume of a gas is proportional to the absolute temperature.**

Gay-Lussac’s second law is a direct consequence of Charles’s law, which establishes the relationship between the volume and the temperature of a gas at constant pressure. According to Charles’s law, at constant pressure, the volume of a gas varies in direct proportion to the absolute temperature. In other words, if the absolute temperature of the gas is doubled, **its volume doubles as well.**

Gay-Lussac’s second law is very important in thermodynamics and in physics in general, since it allows us to understand the behavior of gases and their relationship with temperature and volume. Furthermore, this law is used in many practical applications, such as in the construction of motors of **internal combustion and in the production of liquid helium.**

## What is the formula that Gay Lussac’s law uses?

Gay-Lussac’s law can be expressed using the ideal gas equation of state, which establishes the relationship between pressure, volume, temperature and the amount of gas. **This equation is written as:**

*P = nRT/V*

Where** P is the gas pressure**,

*no*is the amount of gas in moles,

*V*is the volume of the gas,

*you*is the absolute temperature and

*R.*is the ideal gas constant.

If the volume of the gas is held constant, **the equation reduces to:**

*P/T = k*

Where ** what is the constant of proportion** between the pressure and the temperature of the gas at constant volume, also known as Charles’s law. This equation is the formula used to express Gay-Lussac’s law.

## What is the history of Gay Lussac’s law?

Gay-Lussac’s law is named after the French chemist and physicist Joseph Louis Gay-Lussac, who discovered it in the early 19th century. In 1802 Gay-Lussac performed a series of experiments in which he measured the relationship between the temperature and pressure of a gas at constant volume. He found that as the temperature increased, the**The pressure of the gas also increased.**

Gay-Lussac’s law **first published in 1802** in the scientific journal Annales de Chimie. Later, in 1807, Gay-Lussac established a similar relationship between temperature and volume of a gas at constant pressure, which became known as Gay-Lussac’s second law.

Gay-Lussac’s law is one of the fundamental laws of thermodynamics and is essential to understand the behavior of gases and their relationship with temperature and pressure. Together with Boyle’s law and Charles’ law, Gay-Lussac’s law** It is part of the ideal gas laws.**

## Examples and exercises with Gay Lussac’s law

Next,** two hypothetical exercises will be presented** that involve Gay-Lussac’s law and how this law can be used to solve problems involving the pressure and temperature of a gas at constant volume.

**Exercise 1**: There is a balloon filled with helium with a volume of 2 liters at a pressure of 1 atmosphere at 25 °C. If the balloon is heated to 50°C, what will be the new pressure inside the balloon?

Procedure:

**convert temperature**from Celsius to Kelvin:*25°C + 273 = 298K***Apply Gay-Lussac’s law**:*P1/T1 = P2/T2,*where*P1 = 1 atm*,*T1 = 298K, T2 = 50°C + 273 = 323K***Clear***P2: P2 = (P1 x T2)/T1*= (*1 atm x 323K)/298K ≈ 1.09 atm*

Therefore,** the new pressure inside the balloon will be** approximately *1.09* atmospheres to *50°C*

**Exercise 2:** There is a 5-liter gas tank at a pressure of 2.5 atmospheres at 27 °C. If the tank is cooled to -10°C, what will be the new volume of the tank?

Procedure:

**convert temperature**from Celsius to Kelvin:*27°C + 273 = 300K, -10°C + 273 = 263K***Apply Gay-Lussac’s law**:*P1/T1 = P2/T2,*where*P1 = 2.5 atm,**T1 = 300K, T2 = 263K***Clear***P2: P2 = (P1 x T2)/T1*=*(2.5 atm x 263K)/300K ≈ 2.19 atm*- Use Boyle’s law to
**find the new volume**:*P1V1 = P2V2*where*V1 = 5 liters and P2 = 2.19 atm* **Clear***V2: V2 = (P1 x V1)/P2*=*(2.5 atm x 5 liters)/2.19 atm ≈ 5.72 liters*

Therefore, **the new volume of the tank will be** approximately *5.72* liters to *-10°C*