Thermodynamics
Ideal Gas Law (Molecular)
Ideal gas law in terms of molecules.
Variables
PPa
Pressure
Gas pressure
In SI units: kg/(m·s²)
Allowed values: greater than 0
Vm³
Volume
Container volume
Allowed values: greater than 0
Nunitless
Number of molecules
Total molecules
Allowed values: greater than 0, whole number
kBJ/K
Boltzmann constant
1.38×10⁻²³
In SI units: kg·m²/(s²·K)
Allowed values: greater than 0
TK
Temperature
Absolute temperature
Allowed values: greater than 0
Derivation
PV = NkT where N = nNₐ and k = R/Nₐ.
Your notes
0/5000
Constants in this formula
Check value
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- N = 2 (Number of molecules)
- kB = 1.380 649 × 10⁻²³ J/K (Boltzmann constant)
- T = 3 K (Temperature)
- V = 4 m³ (Volume)
Result: P = 2.070974 × 10⁻²³ Pa
Other thermodynamics formulas with the same quantities
- Mean Free Path (Kinetic Theory) shares Boltzmann constant, Temperature, Pressure
- Pressure (Kinetic Theory) (Kinetic Theory) shares Pressure, Number of molecules, Volume
- Root Mean Square Speed (Kinetic Theory) shares Boltzmann constant, Temperature
- Most Probable Speed (Kinetic Theory) shares Boltzmann constant, Temperature
- Mean Speed (Kinetic Theory) shares Boltzmann constant, Temperature
- Adiabatic Process (First Law) shares Pressure, Volume
Where this formula is listed
- Thermodynamics formulas, under Kinetic Theory.
- In the thermodynamics list it comes after Ideal Gas Law and before Average Kinetic Energy (Gas).
- Thermodynamics formula sheet, one of 34 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Ideal Gas Law (Molecular) formula?
Ideal Gas Law (Molecular) is written PV = Nk_B T. Ideal gas law in terms of molecules. It belongs to Thermodynamics, under Kinetic Theory.
What are the units in PV = Nk_B T?
In SI units, P is pressure, measured in kg/(m·s²); V is volume, measured in m³; N is number of molecules (dimensionless); k_B is boltzmann constant, measured in kg·m²/(s²·K); T is temperature, measured in K.
How is the Ideal Gas Law (Molecular) formula derived?
PV = NkT where N = nNₐ and k = R/Nₐ. The result is PV = Nk_B T.