## Introduction

The combined gas law is a fundamental principle in the field of thermodynamics that describes the behavior of gases under changing conditions of pressure, volume, and temperature. This law combines Boyle’s law, Charles’s law, and Gay-Lussac’s law into a single equation that can be used to predict how gases will behave in various situations.

## Definition of the Combined Gas Law

The combined gas law states that the ratio of the pressure and volume of a gas is directly proportional to the ratio of its temperature and the number of molecules present, while keeping the amount of gas constant. Mathematically, this can be expressed as:

P1V1/T1 = P2V2/T2

## Applications of the Combined Gas Law

The combined gas law can be applied in various real-life scenarios, such as:

- Calculating the final pressure, volume, or temperature of a gas when one of these parameters changes
- Understanding how changes in temperature can affect the pressure and volume of a gas
- Determining the ideal conditions for storing gas under specific temperatures and pressures

## Example

Let’s consider a gas confined in a container at a pressure of 2 atm and a temperature of 300K. If the volume of the container is reduced to half of its original value, what will be the new pressure of the gas?

Using the combined gas law equation, we can calculate the new pressure as follows:

(2 atm)(V1) / (300K) = (P2)(V1/2) / (300K)

2 atm = P2

Therefore, the new pressure of the gas will be 2 atm.

## Case Study: Gas Storage

In the industry, the combined gas law is used to determine the optimal conditions for storing gases to ensure their stability and safety. By understanding how changes in pressure, volume, and temperature can affect the behavior of gases, companies can make informed decisions about the storage and transportation of these substances.

## Conclusion

The combined gas law is a powerful tool for predicting and understanding the behavior of gases in different conditions. By mastering this principle, scientists and engineers can make accurate calculations and informed decisions about the use and storage of gases in various applications.