Energia Interna Gás Ideal
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
U = 3/2 nRT
About this calculator
The Internal Energy Calculator for Ideal Gas determines the internal energy (U) of a monatomic ideal gas using the formula U = (3/2)nRT. Here, n is the number of moles, R is the universal gas constant (8.314 J/mol·K), and T is the absolute temperature in kelvin. The factor 3/2 arises from the equipartition theorem, which assigns (1/2)kT per degree of freedom per particle. Monatomic gases have only three translational degrees of freedom, leading to U = (3/2)nRT.
This calculator is useful in thermodynamics contexts, such as studying isothermal, isochoric, and adiabatic processes. For example, when calculating the change in internal energy during compression or expansion, you can use this tool to find initial and final U. It is especially applicable to noble gases (helium, neon, argon) and other monatomic gases under low pressure and high temperature conditions, where ideal gas behavior holds.
Important precautions: the formula applies only to monatomic ideal gases. For diatomic or polyatomic gases, internal energy includes rotational and vibrational contributions, altering the factor. Additionally, the ideal gas model ignores intermolecular interactions and molecular volumes, being accurate only at low pressures and high temperatures. Ensure you use temperature in kelvin and the correct number of moles, avoiding confusion with mass or volume.
Frequently asked questions
Does the formula work for diatomic gases like oxygen?
No. For diatomic gases, internal energy is U = (5/2)nRT at moderate temperatures due to rotational degrees of freedom. At high temperatures, vibrations also contribute.
What unit should I use for temperature?
Always use kelvin (K). Temperatures in Celsius or Fahrenheit must be converted to kelvin before calculation.
Can I use this calculator for liquids or solids?
No. The formula is specific to ideal gases. Liquids and solids have complex molecular interactions requiring other models.
What does 'monatomic' mean?
Monatomic means each gas molecule consists of a single atom, such as helium, neon, or argon. These gases have only translational motion.
How do I calculate the change in internal energy in a process?
Calculate initial and final U using the formula and subtract. Since U depends only on temperature, the change is ΔU = (3/2)nRΔT.