Ideal Gas Law Formula

The ideal gas law relates the pressure, volume, temperature, and amount of an ideal gas in one equation.

The Formula

P V = n R T

When to use: If you squeeze a gas, heat it, or add more particles, the other gas properties must adjust in a predictable way.

Quick Example

Pumping air into a bicycle tire adds gas particles to nearly the same volume, so the pressure rises.

Notation

P

is pressure,

V

is volume,

n

is amount in moles,

R

is the gas constant, and

T

is absolute temperature in kelvin.

What This Formula Means

The ideal gas law relates the pressure, volume, temperature, and amount of an ideal gas in one equation.

If you squeeze a gas, heat it, or add more particles, the other gas properties must adjust in a predictable way.

Formal View

For an ideal gas,

PV = nRT

, where

R

is the universal gas constant. The model assumes particles with negligible volume and no intermolecular forces.

Worked Examples

Example 1

medium

A gas at

P_1=200000 \text{ Pa}

V_1=0.1 \text{ m}^3

T_1=400 \text{ K}

is moved to

V_2=0.05 \text{ m}^3

T_2=300 \text{ K}

. Find

P_2

Answer

P_{2} = 300000 Pa

First step

Combined gas law:

\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}

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Example 2

medium

A gas does work expanding from

0.02 \text{ m}^3

0.05 \text{ m}^3

at constant pressure

150000 \text{ Pa}

. Find

W

Example 3

medium

Why does substituting

25^\circ\text{C}

instead of

298 \text{ K}

into

PV=nRT

give a wrong pressure by what factor (roughly), if everything else is correct?

Common Mistakes

Substituting Celsius instead of kelvin for temperature. - Fix this by naming the system, checking "Am I tracking thermal energy transfer, particle motion, temperature change, or pressure-volume-temperature relationships?", and attaching units or direction to the final statement.
Using inconsistent pressure and volume units with the chosen gas constant. - Fix this by naming the system, checking "Am I tracking thermal energy transfer, particle motion, temperature change, or pressure-volume-temperature relationships?", and attaching units or direction to the final statement.
Using ideal gas law from a keyword alone - Signal words like heat, temperature, thermal only point to a possible model; the system must match too.
Substituting numbers before defining the system - A formula cannot repair a missing object, boundary, direction, medium, or circuit path.

Why This Formula Matters

Ideal Gas Law helps students interpret everyday heating, cooling, fluids, and gases without confusing temperature with energy. It is also a bridge from visible motion to particle models.

Frequently Asked Questions

What is the Ideal Gas Law formula?

The ideal gas law relates the pressure, volume, temperature, and amount of an ideal gas in one equation.

How do you use the Ideal Gas Law formula?

If you squeeze a gas, heat it, or add more particles, the other gas properties must adjust in a predictable way.

What do the symbols mean in the Ideal Gas Law formula?

$P$ is pressure, $V$ is volume, $n$ is amount in moles, $R$ is the gas constant, and $T$ is absolute temperature in kelvin.

Why is the Ideal Gas Law formula important in Physics?

Ideal Gas Law helps students interpret everyday heating, cooling, fluids, and gases without confusing temperature with energy. It is also a bridge from visible motion to particle models.

What do students get wrong about Ideal Gas Law?

Students often know a formula related to ideal gas law but skip the recognition step: Am I tracking thermal energy transfer, particle motion, temperature change, or pressure-volume-temperature relationships? That leads to a correct-looking substitution attached to the wrong physical model.

What should I learn before the Ideal Gas Law formula?

Before studying the Ideal Gas Law formula, you should understand: pressure, temperature.

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