Plain-English Meaning
Squeeze a gas into a smaller space (smaller V) and the pressure goes up. Heat it up (higher T) and the pressure also goes up. PV = nRT links all four quantities: Pressure, Volume, moles (n), and Temperature. R = 8.314 J/(mol·K) is the gas constant.
Write the system boundary first. Many thermodynamics mistakes disappear once you know what counts as heat, work, and internal-energy change.
Deeper Explanation
Derived from combining Boyle's law (PV = const at fixed T), Charles' law (V∝T at fixed P), and Avogadro's law. Equivalently PV = Nk_BT where N is number of molecules. An ideal gas has no intermolecular forces and negligible molecular volume — real gases deviate at high P or low T.
Worked Example
Problem: 2 moles of ideal gas at 300 K occupy 0.05 m³. Find the pressure.
- PV = nRT
- P = nRT/V
- P = 2 × 8.314 × 300 / 0.05
- P = 4988.4 / 0.05 = 99,768 Pa
Result: P ≈ 99.8 kPa ≈ 1 atm
Study Next
Open the full formula deep dive
Take a 10-question quiz on this area
At A Glance
Category: Thermodynamics
Levels covered: High School, College, Masters, PhD
Best use: Start with the formula meaning, then move to the worked example and quiz so the equation turns into a tool instead of a memorised line.