1. What is the Temperature of One Gas Molecule Formula?

The temperature of one gas molecule formula relates the kinetic energy of a gas molecule to its temperature using Boltzmann's constant. This formula is derived from the kinetic theory of gases and provides a fundamental relationship between molecular motion and temperature.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( T_g \) — Temperature of gas (Kelvin)
• \( KE \) — Kinetic energy of the gas molecule (Joules)
• \( k \) — Boltzmann's constant (1.38064852 × 10⁻²³ J/K)

Explanation: This equation shows how the temperature of a gas is directly proportional to the average kinetic energy of its molecules, with Boltzmann's constant serving as the proportionality factor.

3. Importance of Temperature Calculation

Details: Understanding the relationship between molecular kinetic energy and temperature is fundamental to thermodynamics and statistical mechanics. It helps explain gas behavior, heat transfer, and energy distribution in molecular systems.

4. Using the Calculator

Tips: Enter the kinetic energy of the gas molecule in Joules. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is Boltzmann's constant?
A: Boltzmann's constant (k) is a fundamental physical constant that relates the average kinetic energy of particles in a gas with the temperature of the gas. Its value is approximately 1.38064852 × 10⁻²³ J/K.

Q2: Why is there a factor of 2/3 in the formula?
A: The factor 2/3 comes from the equipartition theorem, which states that each degree of freedom contributes ½kT to the average energy. For a monatomic gas with three translational degrees of freedom, the total kinetic energy is (3/2)kT.

Q3: Does this formula work for all gases?
A: This formula is most accurate for ideal monatomic gases. For polyatomic gases, additional factors related to rotational and vibrational energy must be considered.

Q4: What are typical values for molecular kinetic energy?
A: At room temperature (300K), the average kinetic energy of a gas molecule is about 6.21 × 10⁻²¹ J.

Q5: How is this related to the ideal gas law?
A: The kinetic theory of gases, from which this formula is derived, provides a molecular explanation for the macroscopic behavior described by the ideal gas law (PV = nRT).