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The internal energy of a monoatomic system represents the total energy contained within the system due to the kinetic energy of its atoms. For ideal monoatomic gases, this energy depends solely on temperature and follows the equipartition theorem.
The calculator uses the formula:
Where:
Explanation: The factor 3/2 comes from the three translational degrees of freedom for monoatomic gases, each contributing ½kT to the total energy according to the equipartition theorem.
Details: Calculating internal energy is fundamental in thermodynamics for understanding heat transfer, work done by systems, and predicting system behavior under different thermal conditions.
Tips: Enter temperature in Kelvin. The temperature must be a positive value greater than 0. The calculator will compute the internal energy using Boltzmann's constant.
Q1: Why is the factor 3/2 used for monoatomic gases?
A: Monoatomic gases have three translational degrees of freedom (x, y, z directions), each contributing ½kT to the internal energy, resulting in 3/2 kT per atom.
Q2: How does this differ from diatomic or polyatomic gases?
A: Diatomic gases have additional rotational degrees of freedom, giving them 5/2 kT per molecule, while polyatomic gases can have even more degrees of freedom.
Q3: What are typical internal energy values?
A: At room temperature (300K), the internal energy per atom is approximately 6.21 × 10⁻²¹ J, which is very small but significant when multiplied by Avogadro's number.
Q4: Does this formula work for real gases?
A: This formula is ideal for ideal gases. Real gases may have additional contributions from intermolecular forces and other factors.
Q5: How is internal energy related to temperature?
A: For ideal monoatomic gases, internal energy is directly proportional to temperature. Doubling the temperature doubles the internal energy.