Average Thermal Energy of Non-linear Polyatomic Gas Molecule Calculator

Thermal Energy Formula:

\[ Q = \left(\frac{3}{2}k_BT\right) + \left(\frac{1}{2}I_y\omega_y^2 + \frac{1}{2}I_z\omega_z^2\right) + \left((3N-6)k_BT\right) \]

Temperature (T):

Moment of Inertia (I_y):

kg·m²

Angular Velocity (ω_y):

rad/s

Moment of Inertia (I_z):

kg·m²

Angular Velocity (ω_z):

rad/s

Atomicity (N):

Thermal Energy (Q):

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1. What is Thermal Energy of Non-linear Polyatomic Gas Molecule?

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

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

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Q = \left(\frac{3}{2}k_BT\right) + \left(\frac{1}{2}I_y\omega_y^2 + \frac{1}{2}I_z\omega_z^2\right) + \left((3N-6)k_BT\right) \]

Where:

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

Explanation: The formula sums three components: translational energy (3/2 kBT), rotational energy (1/2 Iω² terms), and vibrational energy ((3N-6)kBT).

3. Importance of Thermal Energy Calculation

Details: Understanding thermal energy distribution helps predict molecular behavior, heat capacity, 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 (minimum 3 for non-linear molecules).

5. Frequently Asked Questions (FAQ)

Q1: Why is atomicity important in this calculation?
A: Atomicity determines the number of vibrational degrees of freedom (3N-6 for non-linear molecules).

Q2: What if my molecule is linear?
A: For linear molecules, the formula changes - use (3N-5) for vibrational degrees instead of (3N-6).

Q3: What's the significance of the Boltzmann constant?
A: It relates temperature to energy at the molecular level (energy per degree of freedom).

Q4: Can I set angular velocity to zero?
A: Yes, if there's no rotational motion, but non-linear molecules typically have rotational energy at T > 0K.

Q5: Why are there only two rotational terms?
A: For non-linear molecules, there are three rotational degrees of freedom, but we've simplified to two in this calculator.