Average Thermal Energy of Linear Polyatomic Gas Molecule Calculator

Thermal Energy Formula:

\[ Q_{in} = \frac{3}{2}k_BT + \left(\frac{1}{2}I_y\omega_y^2 + \frac{1}{2}I_z\omega_z^2\right) + (3N - 5)k_BT \]

Temperature:

Moment of Inertia (Y-axis):

kg·m²

Angular Velocity (Y-axis):

rad/s

Moment of Inertia (Z-axis):

kg·m²

Angular Velocity (Z-axis):

rad/s

Atomicity:

Thermal Energy:

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1. What is Average Thermal Energy of Linear Polyatomic Gas Molecule?

Definition: This calculator computes the average thermal energy of a linear polyatomic gas molecule, considering translational, rotational, and vibrational degrees of freedom.

Purpose: It helps physicists and chemists understand the energy distribution in polyatomic gas molecules at a given temperature.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Q_{in} = \frac{3}{2}k_BT + \left(\frac{1}{2}I_y\omega_y^2 + \frac{1}{2}I_z\omega_z^2\right) + (3N - 5)k_BT \]

Where:

\( Q_{in} \) — Thermal energy (J)
\( k_B \) — Boltzmann constant (1.38064852×10⁻²³ J/K)
\( T \) — Temperature (K)
\( I_y, I_z \) — Moments of inertia (kg·m²)
\( \omega_y, \omega_z \) — Angular velocities (rad/s)
\( N \) — Atomicity (number of atoms in molecule)

Explanation: The formula accounts for translational (3/2 kBT), rotational (½Iω² terms), and vibrational ((3N-5)kBT) energy contributions.

3. Importance of Thermal Energy Calculation

Details: Understanding thermal energy distribution helps predict molecular behavior, reaction rates, and thermodynamic properties of gases.

4. Using the Calculator

Tips: Enter temperature in Kelvin, moments of inertia in kg·m², angular velocities in rad/s, and atomicity (number of atoms in molecule).

5. Frequently Asked Questions (FAQ)

Q1: What is atomicity in this context?
A: Atomicity refers to the number of atoms in the polyatomic gas molecule (e.g., 2 for diatomic, 3 for triatomic).

Q2: Why are there two rotational terms?
A: For linear molecules, rotation about two perpendicular axes (Y and Z) contributes to the energy.

Q3: What if my molecule is nonlinear?
A: The formula would change - this calculator is specifically for linear polyatomic molecules.

Q4: Why is the vibrational term (3N-5)kBT?
A: For linear molecules, there are 3N-5 vibrational degrees of freedom (3N total minus 3 translational minus 2 rotational).

Q5: What are typical values for moments of inertia?
A: For small molecules, moments of inertia are typically in the range of 10⁻⁴⁷ to 10⁻⁴⁵ kg·m².