# What is Gay-Lussac’s Law? – Example, Derivation

## Introduction

Gas laws play a crucial role in understanding the behavior of gases under different conditions. One such fundamental gas law is Gay-Lussac’s Law, which focuses on the relationship between the pressure and temperature of a gas. In this blog post, we will delve into the intricacies of Gay-Lussac’s Law, exploring its definition, examples, formula, and even its derivation. Let’s unravel the mysteries of this law together!

## What is Gay-Lussac’s Law?

Gay-Lussac’s Law, also known as the pressure-temperature law, states that the pressure of a gas held at constant volume is directly proportional to its temperature, in kelvin. In simpler terms, as the temperature of a gas increases, so does its pressure, assuming the volume remains constant. This phenomenon can be observed in various real-world scenarios involving gases.

### Examples of Gay-Lussac’s Law

Here are a few best examples of Gay-Lussac’s Law for better understanding,

• Example 1: Consider a fixed volume of gas inside a sealed container. If the temperature of the gas is increased, the pressure inside the container will also rise.
• Example 2: In a hot air balloon, as the air inside the balloon is heated, the pressure increases, causing the balloon to ascend due to the buoyant force exerted.

## Gay-Lussac’s Law Formula

Gay-Lussac’s Law can be mathematically represented by the formula:

$$\frac{ P_{1} }{ T_{1} } = \frac{ P_{2} }{ T_{2} }$$

• Where P1 and T1 are, the initial pressure and temperature of the gas, respectively.
• P2 and T2 are the final pressure and temperature of the gas, respectively.

As the temperature (T) of a gas increases, the particles of the gas move faster and collide with the walls of the container more frequently, thus exerting a higher pressure.

## Derivation of Gay-Lussac’s Law

To derive Gay-Lussac’s Law, we can start from the ideal gas law

$$PV=nRT$$

If we hold the volume (V) constant, the ideal gas law becomes:

$$P = \frac{nRT}{V}$$

Now, if we compare the pressures of the gas at two different temperatures (T1and T2), but at the same volume and number of moles, we get:

$$P_{1} = \frac{nR T_{1} }{V}$$ $$P_{2} = \frac{nR T_{2} }{V}$$

Dividing P1 with T1 and P2 with T2

$$\frac{ P_{1}}{T_{1}} = \frac{nR}{V}$$ $$\frac{ P_{2}}{T_{2}} = \frac{nR}{V}$$

We know that nR/V is constant. So,

$$\frac{ P_{1}}{T_{1}}=\frac{ P_{2}}{T_{2}}=K$$

This shows that the ratio of pressure to temperature is constant at a fixed volume and amount of gas, which is the essence of Gay-Lussac’s Law.

## Final Notes

Understanding Gay-Lussac’s Law is essential for comprehending the behavior of gases when subjected to varying temperatures. By grasping the direct proportionality between pressure and temperature at constant volume, we can predict how gases will respond to changes in their environment. Dive deeper into the study of gas laws to unlock a world of scientific wonders!

This article discusses Gay-Lussac’s Law, exploring its unique formula and mathematical derivation in detail. For further exploration of related concepts, we invite you to visit our blog section. For personalized online tuition services, Tutoroot offers exceptional options. Our online chemistry tuition is designed to address any conceptual queries you may have. Click here to schedule a FREE DEMO session.

## FAQs

What is the law of gaseous volume?

The law of gaseous volume, also known as Gay-Lussac’s Law, states that the pressure of a gas held at constant volume is directly proportional to its temperature.

Define Gay Lussac’s Law

Gay-Lussac’s Law relates the pressure of a gas to its temperature at constant volume, showcasing their direct proportionality.

In which law volume is constant?

Gay-Lussac’s Law focuses on the pressure-temperature relationship in a gas system where the volume remains constant.