EngineeringKinetic Theory of GasesUniversity
IBUndergraduate

Thermal Conductivity of Gases Calculator

This equation provides a microscopic estimate of the thermal conductivity of an ideal gas based on kinetic theory parameters.

Use the free calculatorCheck the variablesOpen the advanced solver
Open Advanced Calculator
This is the free calculator preview. Advanced walkthroughs stay in the app.
Result
Ready
Thermal Conductivity

Formula first

Overview

The formula relates the thermal conductivity to the number density of particles , the mean molecular speed , the mean free path , and the Boltzmann constant . It illustrates that in the kinetic theory model, thermal energy transport is governed by the frequency and distance of molecular collisions. This simplified model assumes a dilute gas where particles act as hard spheres.

Symbols

Variables

= Thermal Conductivity, n = Number Density, = Mean Molecular Speed, = Mean Free Path, = Boltzmann Constant

Thermal Conductivity
Number Density
Mean Molecular Speed
m/s
Mean Free Path
Boltzmann Constant
J/K

Apply it well

When To Use

When to use: Use this equation for estimating the thermal conductivity of dilute, monatomic ideal gases where the kinetic theory assumptions hold.

Why it matters: It provides a fundamental physical basis for understanding how microscopic molecular properties like collision frequency and mean free path dictate macroscopic transport phenomena.

Avoid these traps

Common Mistakes

  • Confusing the Boltzmann constant with the thermal conductivity symbol .
  • Neglecting to convert units for number density to particles per cubic meter.
  • Applying the formula to dense gases or liquids where the mean free path approximation is invalid.

One free problem

Practice Problem

Calculate the thermal conductivity of a gas with a number density of 2.5e25 m^-3, a mean molecular speed of 450 m/s, and a mean free path of 1.0e-7 m. (Use = 1.38e-23 J/K)

Number Density2.5e+25 m^-3
Mean Molecular Speed450 m/s
Mean Free Path1e-7 m
Boltzmann Constant1.38e-23 J/K

Solve for:

Hint: Multiply the four values and divide by 2.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Reif, F. (1965). Fundamentals of Statistical and Thermal Physics. McGraw-Hill.
  2. Chapman, S., & Cowling, T. G. (1970). The Mathematical Theory of Non-Uniform Gases. Cambridge University Press.
  3. Kinetic Theory of Gases
  4. NIST CODATA Recommended Values
  5. IUPAC Gold Book
  6. Wikipedia: Thermal conductivity
  7. Wikipedia: Kinetic theory of gases
  8. Halliday, David; Resnick, Robert; Walker, Jearl. Fundamentals of Physics.