Root-Mean-Square Temperature

The Temperature of Gaseous Particles calculator uses the root-mean-square speed equation to compute the temperature based on the molecular speed, molar mass and the ideal gas constant.

INSTRUCTIONS: Choose units and enter the following:

• (v) Molecular Speed
• (M) Molar mass

Temperature (T): The calculator returns the temperature in degrees Kelvin.  However, this can be automatically converted to compatible units via the pull-down menu.

Related Calculators

• Compute the Temperature of gas based on the Root-Mean-Square formula
• Compute the molecular speed of a gas based on the Root-Mean-Square formula
• R-Gas Constant with SI Units

The Math / Science

The Root-Mean-Square Speed formula for the molecular speed of gaseous particles is:

           `V=sqrt((3*R*T)/M)`

where:

• V is the molecular speed of gas particles
• T is the temperature with units of K
• M is molar mass in kilograms per mole (kg/mol)
• R is the ideal gas constant (8.314 kg*m² / mol*K*s)

This calculator uses the above formula solved for temperature:

             T = (M•V²)/(3•R)

Reference

Whitten, et al. "Chemistry" 10th Edition. Pp. 433

UCDavis ChemWiki: Connecting Gas Properties to Kinetic Theory of Gases