## Gay- Lussac's Law

**Gay-Lussac's law:** In Physical chemistry, we study four different types of gas law, namely, Boyle's Law, Charles's Law, Gay-Lussac Law and Avogadro's Law. These laws are the results of research carried out for many centuries on the physical properties of gases. The foremost reliable measurement of the properties of gases was made by an Anglo-Irish scientist named Robert Boyle in the year 1662. The law which he formulated is referred to as Boyle’s Law. Later on, attempts related to knowing the other properties of gases lead Jacques Charles and Joseph Lewis Gay Lussac to discover new additional gas laws such as Charles Law and Gay Lussac Law. Also, Avogadro provided a lot of information related to gaseous laws. So in this article, we will discuss Gay Lussac's Law in detail.

## What is Gay-Lussac's Law?

You would have seen the pressure in the tyre almost remains constant but during hot days the pressure may increase resulting in the bursting of the tyre and during winter days the reverse happens, that is, the pressure of the tyre decreases.** Joseph Gay- Lussac formulated the concept to give the relationship between pressure and temperature which came to be known as Gay-Lussca Law.** **This law states that, at constant volume, the pressure of a fixed amount of a gas is directly proportional to the temperature.** Mathematically it can be written as-

**P ∝ T**

## Formula and Derivation of Gay-Lussac's Law

At constant volume, the pressure of a fixed amount of a gas is directly proportional to the temperature. Mathematically it can be written as-

**P ∝ T**

By removing the proportionality constant we get,

**P/T = k**

k is the proportionality constant

P indicates the pressure exerted by the gas

T is the temperature

At two different points, we can relate pressure and temperature then because they are both equal to the same constant value. That is:

P1/T1 = k ………(1)

and, P2/T2 = k ………..(2)

Equating (1) and (2)

**P1/T1 = P2/T2 = k**

**P1T2 = P2T1**

## Application of Gay-Lussac's Law

The application of the gay-Lussac law is as follows-

- The heating of aerosol can causes an increase in temperature which further causes the gases to change it can lead to an explosion of the can, therefore here also Gay-Lussac law applies.
- The firing of a bullet causes the gases trapped inside to fire at tremendous force toward the gun's barrel.
- We can see the application of the Gay Lussac Law in the burning of an automobile tyre.
- While cooking, the increased pressure in a pressure cooker is another example where we apply Gay Lussac Law.

## Solved Examples of Gay-Lussac's Law

**Example 1:** The pressure of a gas when it is heated to a temperature of 450K is 5 atm. What will be the initial temperature of the gas if the initial pressure was 3atm?

**Solution:** According to the question, Initial pressure be P1 = 3 atm

Final pressure, that is P2 be = 5 atm

Final temperature, that is T2 be = 450 K

According to Gay-Lussac’s Law,

P1T2 = P2T1

3 x 450 = 5 x T1

T1 = 3 x 450/5

T1 = 3 x 90

**T1 = 270 K**

**Example 2: At a temperature of 500 K, the pressure of the gas in a spray is 5 atm. Calculate the pressure of the gas when it is heated to 800 K.**

**Solution:** According to the question,

Initial pressure, that is, P1 = 5 atm

Initial temperature, that is, T1 = 500K

Final temperature, that is, T2 = 800 K

**Hence the final pressure (P2) = (P1T2)/T1 = 5 x 800/500 = 8 atm.**

**Example 3: The gas in a pressure cooker is under a pressure of 8.00atm at a temperature of 15°C. What would the pressure be in the pressure cooker at a temperature of 345°C?**

Solution: According to the question,

Initial pressure, that is, P1= 8.00atm

Initial temperature, that is, T1 = 15°C = 15 + 273.15 = 288.15 K

Final temperature, that is, T2 = 345°C = 345 +2 73.15 = 618.15 K

**Final Pressure(P2) = (P1T2)/T1 = 17.16 atm**