Gay Lussac's Law Calculator

What is Gay-Lussac’s Law?

Gay-Lussac’s Law, named after the French chemist Joseph Louis Gay-Lussac, explains how the pressure of a gas changes with its temperature when the volume is kept constant. Simply put, if you heat a gas in a sealed container, its pressure will go up. If you cool it down, the pressure will decrease.

The Basic Idea

Imagine you have a bike tire. If you leave it out in the hot sun, the air inside the tire gets warmer, and the tire feels harder because the pressure inside goes up.

Now, if you were to take that same tire into a cold garage, the air cools, and the tire might feel softer because the pressure drops. This is Gay-Lussac’s Law in action!

The Formula

A gas initially has a pressure of 2.0 atm and a temperature of 300 K. If the temperature increases to 450 K, what will be the new pressure of the gas?

Solution:

Using Gay-Lussac’s Law:

\[\frac{P_1}{T_1} = \frac{P_2}{T_2}\]

Substituting the known values:

\[\frac{2.0 \text{ atm}}{300 \text{ K}} = \frac{P_2}{450 \text{ K}}\]

Solving for \( P_2 \):

\[P_2 = \frac{2.0 \times 450}{300} = 3.0 \text{ atm}\]

The new pressure is 3.0 atm.

Practical Applications

Weather Balloons: They expand as they rise into colder parts of the atmosphere but can also burst if they get too hot due to increased pressure.

Pressure Cookers: They use this principle to cook food faster by increasing the boiling point of water inside the sealed pot.

Advanced Considerations

Ideal Gas Behavior: Gay-Lussac’s Law assumes ideal gas behavior, where gas particles don’t interact much except during collisions. Real gases might deviate from this law at very high pressures or low temperatures.
Real World vs. Ideal: In the real world, you might need to account for leaks, changes in volume due to material expansion, or non-ideal gas behavior.