# Charles' Law Example Problem

## Real-life applications for the ideal gas law at constant pressure Charles's Law is a special case of the Ideal Gas Law at constant pressure. Paul Taylor, Getty Images

Charles' law is a special case of the ideal gas law in which the pressure of a gas is constant. Charles' law states that volume is proportional to the absolute temperature of a gas at constant pressure. Doubling the temperature of gas doubles its volume, so long as the pressure and quantity of the gas are unchanged.

## Charles' Law Example Problem

This example problem shows how to use Charles' law to solve a gas law problem: A 600 mL sample of nitrogen is heated from 27 °C to 77 °C at constant pressure. What is the final volume?

Solution:

The first step to solving gas law problems should be converting all temperatures to absolute temperatures. In other words, if the temperature is given in Celsius or Fahrenheit, convert it to Kelvin. (This is where the most commonplace mistakes are made in this type of homework problem.)

T K = 273 + °C
Ti = initial temperature = 27 °C
Ti K = 273 + 27
Ti K = 300 K
Tf = final temperature = 77 °C
Tf K = 273 + 77
Tf K = 350 K

The next step is to use Charles' law to find the final volume. Charles' law is expressed as:

Vi/Ti = Vf/Tf
where
Vi and Ti is the initial volume and temperature
Vf and Tf is the final volume and temperature
Solve the equation for Vf:
Vf = ViTf/Ti
Enter the known values and solve for Vf.
Vf = (600 mL)(350 K)/(300 K)
Vf = 700 mL
The final volume after heating will be 700 mL.

## More Examples of Charles' Law

If you think Charles' Law seems irrelevant to real-life situations, think again! By understanding the basics of the law, you'll know what to expect in a variety of real-world situations and once you know how to solve a problem using Charles' Law, you can make predictions and even start to plan new inventions. Here are several examples of situations in which Charles' Law is at play:

• If you take a basketball outside on a cold day, the ball shrinks a bit as the temperature is decreased. This is also the case with any inflated object and explains why it's a good idea to check your car's tire pressure when the temperature drops.
• If you over-inflate a pool float on a hot day, it can swell in the sun and burst.
• Pop-up turkey thermometers work based on Charles' law. As the turkey cooks, the gas inside the thermometer expands until it can "pop" the plunger.

## Examples of Other Gas Laws

Charles' law is only one of the special cases of the ideal gas law that you may encounter. Each of the laws is named for the person who formulated it. It's good to know how to tell the gas laws apart and be able to cite examples of each one.

• Amonton's Law: Doubling temperature doubles pressure at constant volume and mass. Example: As automobile tires heat up when you drive, their pressure increases.
• Boyle's Law: Doubling pressure halves volume, at constant temperature and mass. Example: When you blow bubbles underwater, they expand as they rise to the surface.
• Avogadro's Law: Doubling the mass or number of moles of a gas doubles the volume at constant temperature and pressure. Example: Inhaling fills the lungs with air, expanding their volume.