The ideal gas law is an equation of state that describes the behavior of an ideal gas. It establishes a relationship between pressure (P), volume (V), amount of substance (n), and absolute temperature (T) through the universal gas constant (R).
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How to measure it in class
With the FizziQ app, you can experimentally verify the ideal gas law by measuring atmospheric pressure and studying its variations.
Steps:
- Use the FizziQ barometer to measure atmospheric pressure at different altitudes
- Observe pressure variations when climbing stairs or riding an elevator
- Measure ambient temperature with the temperature sensor
- Calculate the P/T ratio and verify it remains constant at fixed volume
- Compare measured values with predictions from the ideal gas law
Scientific activities on this topic
The ideal gas law can be explored through several experimental activities:
- Gas law: https://www.fizziq.org/en/activities/gas-law/
- Toilets and atmospheric pressure: https://www.fizziq.org/en/activities/toilets-and-atmospheric-pressure/
- Altimeter: https://www.fizziq.org/en/activities/altimeter/
- Study of the pressure-altitude relationship in the atmosphere
Learn more
Historical gas laws:
The ideal gas law is a synthesis of several experimental laws discovered between the 17th and 19th centuries:
Boyle’s Law (1662): At constant temperature, the product of pressure and volume of a gas is constant: PV = constant. This law shows that when a gas is compressed, its pressure increases proportionally.
Charles’s Law (1787): At constant pressure, the volume of a gas is proportional to its absolute temperature: V/T = constant. Jacques Charles discovered that gases expand uniformly with temperature.
Gay-Lussac’s Law (1802): At constant volume, the pressure of a gas is proportional to its absolute temperature: P/T = constant.
Avogadro’s Law (1811): At equal temperature and pressure, equal volumes of gases contain the same number of molecules.
The ideal gas:
An ideal gas is an idealized model where:
- Molecules are considered as point particles with no volume
- Interactions between molecules are neglected (except during elastic collisions)
- The average kinetic energy of molecules is proportional to temperature
Real gases (air, oxygen, nitrogen) behave like ideal gases at low pressure and high temperature. At high pressure or low temperature, corrections are needed (Van der Waals equation).
Applications:
The ideal gas law is fundamental in meteorology, chemistry, atmospheric physics, and engineering. It allows calculating air density, understanding how heat engines work, and explaining atmospheric phenomena.
Formula
Ideal gas equation:
PV = nRT
where:
- P: gas pressure (Pa)
- V: gas volume (m³)
- n: amount of substance (mol)
- R: universal gas constant (8.314 J·mol⁻¹·K⁻¹)
- T: absolute temperature (K)
Alternative form with mass:
PV = (m/M)RT
where m is the gas mass and M is the molar mass.
For air at 20°C and 1 atm: ρ ≈ 1.2 kg/m³
Application examples
- Calculating tire pressure as a function of temperature
- Sizing scuba diving tanks
- Predicting weather balloon expansion at altitude
- Internal combustion engine operation
- Calculating altitude from atmospheric pressure (barometric altimetry)
- Gas compression and expansion in refrigerators
FAQ
Q: Why do we use temperature in Kelvin? A: The ideal gas law requires an absolute temperature scale because it relies on the kinetic energy of molecules. At 0 K (absolute zero), molecules have no kinetic energy. The Celsius scale would give incorrect results because 0°C is not the absence of molecular motion.
Q: What is the constant R? A: R is the universal gas constant, equal to 8.314 J·mol⁻¹·K⁻¹. It relates thermal energy to temperature and amount of substance. R = NA × kB where NA is Avogadro’s number and kB is Boltzmann’s constant.
Q: Is air an ideal gas? A: Air behaves as an ideal gas under normal temperature and pressure conditions. Deviations become significant at very high pressure (>100 atm) or very low temperature (near the liquefaction point).
Q: Why do tires inflate when it’s hot? A: At nearly constant volume, Gay-Lussac’s law (P/T = constant) predicts that pressure increases with temperature. A 10°C increase can raise pressure by about 0.1 bar.
Q: How does the gas law explain altimetry? A: Atmospheric pressure decreases with altitude because the air column above is shorter. By combining the ideal gas law with hydrostatic equilibrium, we obtain the barometric formula relating pressure and altitude.
Related concepts
Atmospheric pressure - Absolute temperature - Absolute zero - Density - Molar volume - Boltzmann constant - Van der Waals equation - Thermodynamics