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Before this: Boyle's law

Charles’s law

At constant pressure, the volume of a fixed amount of gas is directly proportional to its temperature in kelvins.

V1 / T1 = V2 / T2

Heating a gas makes its particles move faster and hit the walls harder. If the container can expand, it does, until the pressure inside matches the pressure outside again.

Worked example: warming a balloon

A balloon has a volume of 2.00 L at 300 K. What is its volume at 450 K, at the same pressure?

V1 / T1 = V2 / T2

2.00 L / 300 K = V2 / 450 K

V2 = 2.00 L × 450 K ÷ 300 K = 3.00 L

Check: the temperature went up, so the volume should go up. It did.

When pressure, volume and temperature all change, use the combined gas law:

P1 × V1 / T1 = P2 × V2 / T2

Common mistake

Using degrees Celsius. Going from 20 °C to 40 °C does not double the volume. In kelvins that is 293 K to 313 K, an increase of about 7%.

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Watch Heating a gas at constant pressure
  1. A balloon's worth of gas: 2.00 L at 300 K. The pressure stays at 1.00 atm throughout.
  2. Warm it to 375 K. The particles hit harder, the piston rises, and the volume grows to 2.50 L.
  3. At 450 K the volume is 3.00 L, the answer to the worked example.
  4. At every step, V ÷ T came to the same value: 0.00667 L/K.

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Explore Heat a gas

Change the temperature and watch the volume. The pressure stays constant.

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Practice

1. A gas occupies 3.00 L at 200 K. What is its volume at 400 K, at constant pressure?

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2. A gas occupies 5.00 L at 27 °C. What is its volume at 127 °C, at constant pressure?

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3. A gas has a volume of 2.00 L at 1.00 atm and 300 K. What is its volume at 2.00 atm and 600 K?

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4. A sealed balloon is moved from a warm room into a freezer. Its volume:

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