Gay-Lussac's Law

Gay-Lussac's Law describes the relationship between the pressure and temperature of a gas at constant volume. It can be expressed mathematically as:

center;">P1/T1 = P2/T2

• P1 = initial pressure
• T1 = initial temperature (in Kelvin)
• P2 = final pressure
• T2 = final temperature (in Kelvin)

Key Concepts:

1. Gay-Lussac's Law applies to a gas at constant volume.
2. As the temperature of a gas increases, its pressure also increases proportionally, and vice versa.
3. The temperature must be in Kelvin for the law to hold true. To convert from Celsius to Kelvin, add 273.15 to the Celsius temperature.
4. Gases behave more ideally at higher temperatures and lower pressures.

Example:

If a gas has an initial pressure of 2 atm at a temperature of 300 K, what will be its pressure if the temperature is increased to 400 K?

Using the formula P1/T1 = P2/T2, we can solve for P2:

center;">2 atm / 300 K = P2 / 400 K

center;">P2 = (2 atm * 400 K) / 300 K

center;">P2 = 2.67 atm

So, the pressure of the gas at 400 K will be 2.67 atm.

Applications:

• Gay-Lussac's Law is used in various industrial and scientific applications, such as in the design and operation of pressurized containers, air conditioning systems, and chemical reactions involving gases.
• Understanding the behavior of gases under changing temperature and pressure conditions is crucial for safety and efficiency in many engineering processes.