Thermal Energy Formula:
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Definition: This calculator computes the average thermal energy of a non-linear polyatomic gas molecule based on its atomicity and temperature.
Purpose: It helps in understanding the energy distribution in polyatomic gas molecules, important in thermodynamics and statistical mechanics.
The calculator uses the formula:
Where:
Explanation: For non-linear polyatomic molecules, there are 3N-6 vibrational degrees of freedom contributing to the thermal energy.
Details: Understanding thermal energy helps predict molecular behavior, heat capacity, and energy distribution in gases.
Tips: Enter the atomicity (must be ≥3 for non-linear molecules) and temperature in Kelvin. All values must be positive.
Q1: Why is atomicity limited to ≥3?
A: This calculator is specifically for non-linear polyatomic molecules, which require at least 3 atoms (diatomic and monatomic molecules have different energy calculations).
Q2: What's the significance of the Boltzmann constant?
A: It relates temperature to energy at the molecular level, fundamental in statistical mechanics.
Q3: Why 6N-6 in the formula?
A: Non-linear molecules have 3 translational, 3 rotational, and 3N-6 vibrational degrees of freedom. The formula accounts for all these energy contributions.
Q4: How does temperature affect the result?
A: Thermal energy is directly proportional to temperature - higher temperature means greater thermal energy.
Q5: What are typical values for polyatomic molecules?
A: Common polyatomic gases like CO₂ (N=3), CH₄ (N=5), or C₆H₆ (N=12) would have increasing thermal energy with higher atomicity.