Charles' law is a special case of the ideal gas law where the pressure of a gas is constant. Charles' law states the 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. This example problem shows how to use Charles' law to solve a gas law problem.

### Charles Law Example 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. This is the most common place mistakes are made in this type of homework problem.

T K = 273 + °C

T_{i} = initial temperature = 27 °C

T_{i} K = 273 + 27

T_{i} K = 300 K

T_{f} = final temperature = 77 °C

T_{f} K = 273 + 77

T_{f} K = 350 K

The next step is to use Charles' law to find the final volume. Charles' law is expressed as:**V _{i}/T_{i} = V_{f}/T_{f}**

where

V

_{i}and T

_{i}is the initial volume and temperature

V

_{f}and T

_{f}is the final volume and temperature

Solve the equation for V

_{f}:

V

_{f}= V

_{i}T

_{f}/T

_{i}

Enter the known values and solve for V

_{f}.

V

_{f}= (600 mL)(350 K)/(300 K)

V

_{f}= 700 mL

**Answer:**

The final volume after heating will be 700 mL.

### More Examples of Charles's Law

- If you take a basketball outside on a cold day, the ball shrinks a bit as the temperature is decreased.
- 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 be able to tell the gas laws apart and cite examples of each one.

- As automobile tires heat up during driving, their pressure increases. (Amonton's Law: Doubling temperature doubles pressure at constant volume and mass.)
- When you blow bubbles underwater, they expand as they rise to the surface. (Boyle's Law: Doubling pressure halves volume, at constant temperature and mass.)
- Inhaling fill the lungs with air and expands their volume. (Avogadro's Law: Doubling the mass or number of moles of a gas doubles the volume at constant temperature and pressure.)