Advanced · 13 min
Ideal gases and absolute temperature
Relate gas pressure, volume, and temperature under stated constraints.
Use kelvin for gas ratios
Gas pressure comes from particles exchanging momentum with the container walls. The ideal-gas model treats particles as tiny, with negligible interactions except during collisions. For a fixed amount of ideal gas, pV/T stays constant between equilibrium states. Temperature must be in kelvin, where T = temperature in °C + 273.15. Use absolute pressure, not pressure measured relative to the atmosphere.
Worked example
At fixed volume, a gas at 300 K and 100,000 Pa warms to 450 K. p₂ = 100,000 × 450 ÷ 300 = 150,000 Pa
State what stays fixed
At constant temperature for a fixed amount of ideal gas, p₁V₁ = p₂V₂. Compressing the gas into half the volume doubles its absolute pressure. At constant absolute pressure, volume is proportional to kelvin temperature. The full equation pV = nRT also includes the amount of gas n in moles. Real gases can depart from the ideal model, especially near condensation or at high density.
Worked example
At constant temperature, a gas at 80,000 Pa occupies 0.06 m³. If its volume becomes 0.03 m³, pressure = 80,000 × 0.06 ÷ 0.03 = 160,000 Pa.
Compare two heating conditions
- A fixed amount of ideal gas warms from 300 K to 600 K. Describe what happens to pressure if volume stays fixed.
- Describe what happens to volume instead if absolute pressure stays fixed. Explain why the fixed condition matters.