Thermodynamics
Internal Energy (Ideal Gas)
Internal energy depends only on temperature for ideal gas.
Variables
UJ
Internal energy
Total internal energy
In SI units: kg·m²/s²
funitless
Degrees of freedom
3 mono, 5 diatomic
Allowed values: greater than 0, whole number
nmol
Moles
Amount of gas
Allowed values: greater than 0
RJ/(mol·K)
Gas constant
8.314
In SI units: kg·m²/(s²·mol·K)
Allowed values: greater than 0
TK
Temperature
Absolute temperature
Allowed values: greater than 0
Derivation
From equipartition theorem: each DoF has ½kT energy.
Your notes
0/5000
Constants in this formula
Other thermodynamics formulas with the same quantities
- Work (Isothermal Process) (First Law) shares Moles, Gas constant, Temperature
- Root Mean Square Speed (Kinetic Theory) shares Temperature, Gas constant
- Entropy Change (Ideal Gas) (Entropy) shares Moles, Gas constant
- Helmholtz Free Energy (Entropy) shares Internal energy, Temperature
- Most Probable Speed (Kinetic Theory) shares Temperature, Gas constant
- Mean Speed (Kinetic Theory) shares Temperature, Gas constant
Where this formula is listed
- Thermodynamics formulas, under First Law, alongside Work Done by Gas, Adiabatic Process, Heat Capacity Relation, Work (Adiabatic Process) and Enthalpy.
- In the thermodynamics list it comes after Work (Isothermal Process) and before Adiabatic Process.
- 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 Internal Energy (Ideal Gas) formula?
Internal Energy (Ideal Gas) is written U = (f/2)nRT. Internal energy depends only on temperature for ideal gas. It belongs to Thermodynamics, under First Law.
What are the units in U = (f/2)nRT?
In SI units, U is internal energy, measured in kg·m²/s²; f is degrees of freedom (dimensionless); n is moles, measured in mol; R is gas constant, measured in kg·m²/(s²·mol·K); T is temperature, measured in K.
How is the Internal Energy (Ideal Gas) formula derived?
From equipartition theorem: each DoF has ½kT energy. The result is U = (f/2)nRT.