Thermodynamics · Quick Reference

Gas Laws Cheat Sheet

Thermodynamics · Lesson 5/10

In one line: the gas laws describe precise relationships between a gas's pressure, volume, temperature, and amount — remarkably simple equations that explain everything from balloons to car engines.

Key Ideas

1Boyle's Law. At constant temperature, pressure and volume are inversely related: P1*V1 = P2*V2.

2Charles's Law. At constant pressure, volume and temperature (in Kelvin) are directly proportional: V1/T1 = V2/T2.

3Gay-Lussac's Law. At constant volume, pressure and temperature (in Kelvin) are directly proportional: P1/T1 = P2/T2.

4The Combined Gas Law. Merges all three: (P1*V1)/T1 = (P2*V2)/T2, useful when pressure, volume, and temperature all change together.

5The Ideal Gas Law. PV = nRT, where n is the number of moles of gas and R is the universal gas constant (8.314 J/(mol*K)) -- relates all four key gas variables at once.

Worked Examples

A gas has volume 4L at pressure 2 atm. Find its volume if pressure increases to 8 atm (constant temperature).

1 L

A gas has volume 2L at 300K. Find its volume at 600K (constant pressure).

4 L

A gas has pressure 1 atm at volume 10L and temperature 250K. Find its pressure at volume 5L and temperature 500K.

4 atm

Formulas

Boyle's Law: P1*V1 = P2*V2

Charles's Law: V1/T1 = V2/T2

Combined gas law: (P1*V1)/T1 = (P2*V2)/T2

Ideal gas law: PV = nRT

Practice Yourself

A gas has volume 6L at pressure 3 atm. Find volume at 9 atm (Boyle's Law).

P1V1=P2V2: 18=9*V2, V2=2L

A gas has volume 3L at 200K. Find volume at 400K (Charles's Law).

3/200=V2/400, V2=6L

What variables does Boyle's Law relate at constant temperature?

Pressure and volume