Thermodynamics
Internal Energy (Ideal Gas)
Internal energy depends only on temperature for ideal gas.
Variables
UJ
Internal energy
Total internal energy
funitless
Degrees of freedom
3 mono, 5 diatomic
nmol
Moles
Amount of gas
RJ/(mol·K)
Gas constant
8.314
TK
Temperature
Absolute temperature
Derivation
From equipartition theorem: each DoF has ½kT energy.
Your notes
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Common questions
What is the Internal Energy (Ideal Gas) formula?
Internal Energy (Ideal Gas) is written U = f/2nRT. Internal energy depends only on temperature for ideal gas. It belongs to Thermodynamics, under First Law.
What are the units in U = f/2nRT?
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/2nRT.