Charles's Law Formula

Charles's law states that for a fixed amount of gas at constant pressure, volume is directly proportional to absolute temperature.

The Formula

\frac{V_1}{T_1} = \frac{V_2}{T_2}

When to use: Warmer gas spreads out more when it is free to expand.

Quick Example

A balloon grows in volume when it warms up because the gas particles move faster.

Notation

V

is volume and

T

is absolute temperature in kelvin. At constant pressure,

V_1/T_1 = V_2/T_2

— volume and temperature are directly proportional.

What This Formula Means

Charles's law states that for a fixed amount of gas at constant pressure, volume is directly proportional to absolute temperature.

Warmer gas spreads out more when it is free to expand.

Worked Examples

Example 1

easy

A weather balloon holds

4.0\text{ L}

of helium at

200\text{ K}

. The balloon is warmed to

300\text{ K}

at constant pressure. What is its new volume?

Answer

V_2 = 6.0\text{ L}

First step

List the knowns:

V_1 = 4.0\text{ L}

T_1 = 200\text{ K}

T_2 = 300\text{ K}

P

constant.

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Example 2

medium

A piston of oxygen reads

480\text{ mL}

-23\,^{\circ}\text{C}

and constant pressure. To what kelvin temperature must it be warmed for the volume to reach

720\text{ mL}

Example 3

medium

Two readings on a hot-air balloon's gas bag at constant pressure: at

290\text{ K}

the bag holds

580\text{ L}

. To make it lift more, the air is heated to

348\text{ K}

. How much larger is the volume?

Common Mistakes

Using Celsius instead of Kelvin - Fix this by naming the substances or sample, checking "Am I comparing gas variables with units and temperature in kelvin, while holding the stated variables constant?", and attaching units, formulas, states, or evidence to the final statement. - Fix this by naming the substances or sample, checking "Am I comparing gas variables with units and temperature in kelvin, while holding the stated variables constant?", and attaching units, formulas, states, or evidence to the final statement.
Applying Charles's law when pressure is not constant - Fix this by naming the substances or sample, checking "Am I comparing gas variables with units and temperature in kelvin, while holding the stated variables constant?", and attaching units, formulas, states, or evidence to the final statement. - Fix this by naming the substances or sample, checking "Am I comparing gas variables with units and temperature in kelvin, while holding the stated variables constant?", and attaching units, formulas, states, or evidence to the final statement.
Assuming the relationship is inverse instead of direct - Fix this by naming the substances or sample, checking "Am I comparing gas variables with units and temperature in kelvin, while holding the stated variables constant?", and attaching units, formulas, states, or evidence to the final statement. - Fix this by naming the substances or sample, checking "Am I comparing gas variables with units and temperature in kelvin, while holding the stated variables constant?", and attaching units, formulas, states, or evidence to the final statement.
Using charles's law from a keyword alone - Signal words like gas, pressure, volume only point to a possible model; the substances and evidence must match too. - Fix this by naming the substances or sample, checking "Am I comparing gas variables with units and temperature in kelvin, while holding the stated variables constant?", and attaching units, formulas, states, or evidence to the final statement.

Why This Formula Matters

Charles's Law helps students reason about gases as particle systems rather than loose formulas. It connects lab measurements to molecular motion and conditions.

Frequently Asked Questions

What is the Charles's Law formula?

Charles's law states that for a fixed amount of gas at constant pressure, volume is directly proportional to absolute temperature.

How do you use the Charles's Law formula?

Warmer gas spreads out more when it is free to expand.

What do the symbols mean in the Charles's Law formula?

$V$ is volume and $T$ is absolute temperature in kelvin. At constant pressure, $V_1/T_1 = V_2/T_2$ — volume and temperature are directly proportional.

Why is the Charles's Law formula important in Chemistry?

Charles's Law helps students reason about gases as particle systems rather than loose formulas. It connects lab measurements to molecular motion and conditions.

What do students get wrong about Charles's Law?

Students often know a formula related to charles's law but skip the recognition step: Am I comparing gas variables with units and temperature in kelvin, while holding the stated variables constant? That leads to a correct-looking substitution attached to the wrong chemical model.

What should I learn before the Charles's Law formula?

Before studying the Charles's Law formula, you should understand: gas laws.

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Related Concepts

Gas Laws Avogadro's Law

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Gas Laws Formula Avogadro's Law Formula