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

Definition: This calculator determines the temperature of a linear polyatomic gas molecule based on its thermal energy and atomicity.

Purpose: It helps in understanding the relationship between thermal energy and temperature for complex gas molecules in thermodynamics.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( T \) — Temperature (Kelvin)
• \( Q_{in} \) — Thermal Energy (Joules)
• \( N \) — Atomicity (number of atoms in molecule)
• \( [BoltZ] \) — Boltzmann constant (1.38064852 × 10⁻²³ J/K)

Explanation: The formula accounts for the degrees of freedom in a linear polyatomic molecule and relates thermal energy to temperature through the Boltzmann constant.

3. Importance of This Calculation

Details: Understanding this relationship is crucial in statistical mechanics, thermodynamics, and kinetic theory of gases.

4. Using the Calculator

Tips: Enter the thermal energy in joules and the atomicity (number of atoms in the molecule). Both values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is atomicity in this context?
A: Atomicity refers to the total number of atoms present in a molecule of the gas (e.g., 2 for O₂, 3 for CO₂).

Q2: Why is the Boltzmann constant used?
A: The Boltzmann constant relates energy at the particle level to temperature observable at the macroscopic level.

Q3: Does this formula work for all gas molecules?
A: No, this specific formula is for linear polyatomic molecules. Different forms exist for monatomic and nonlinear polyatomic molecules.

Q4: What are typical values for thermal energy?
A: Thermal energy values can vary widely but are often in the range of 10⁻²¹ to 10⁻¹⁹ J for individual molecules.

Q5: Why does the result show very small numbers?
A: The results are small because we're dealing with molecular-scale energies and the tiny Boltzmann constant.