Temperature of Gas given RMS Velocity of Gas Calculator

✖The Root Mean Square Velocity is the square root of the average of the square of the velocity. As such, it has units of velocity.ⓘ Root Mean Square Velocity [V_rms]			+10% -10%
✖Molar Mass is the mass of a given substance divided by the amount of substance.ⓘ Molar Mass [M_molar]			+10% -10%

✖The temperature of Gas is the measure of hotness or coldness of a gas.ⓘ Temperature of Gas given RMS Velocity of Gas [T_g]

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Temperature of Gas given RMS Velocity of Gas Solution

STEP 0: Pre-Calculation Summary

Formula Used

Temperature of Gas = Root Mean Square Velocity^2*Molar Mass/(3*[R])
T_g = V_rms^2*M_molar/(3*[R])
This formula uses 1 Constants, 3 Variables

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Variables Used

Temperature of Gas - (Measured in Kelvin) - The temperature of Gas is the measure of hotness or coldness of a gas.
Root Mean Square Velocity - (Measured in Meter per Second) - The Root Mean Square Velocity is the square root of the average of the square of the velocity. As such, it has units of velocity.
Molar Mass - (Measured in Kilogram Per Mole) - Molar Mass is the mass of a given substance divided by the amount of substance.

STEP 1: Convert Input(s) to Base Unit

Root Mean Square Velocity: 300 Meter per Second --> 300 Meter per Second No Conversion Required
Molar Mass: 44.01 Gram Per Mole --> 0.04401 Kilogram Per Mole (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_g = V_rms^2*M_molar/(3*[R]) --> 300^2*0.04401/(3*[R])

Evaluating ... ...

T_g = 158.795590362911

STEP 3: Convert Result to Output's Unit

158.795590362911 Kelvin --> No Conversion Required

FINAL ANSWER

158.795590362911 ≈ 158.7956 Kelvin <-- Temperature of Gas

(Calculation completed in 00.020 seconds)

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Osmania University (OU), Hyderabad

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Temperature of Gas given RMS Velocity of Gas Formula

LaTeX Go

Temperature of Gas = Root Mean Square Velocity^2*Molar Mass/(3*[R])
T_g = V_rms^2*M_molar/(3*[R])

What is the use of rms speed?

The root-mean-square speed takes into account both molecular weight and temperature, two factors that directly affect the kinetic energy of a material.By squaring the velocities and taking the square root, we overcome the “directional” component of velocity and simultaneously acquire the particles’ average velocity. Since the value excludes the particles’ direction, we now refer to the value as the average speed. The root-mean-square speed is the measure of the speed of particles in a gas, defined as the square root of the average velocity-squared of the molecules in a gas.

How to Calculate Temperature of Gas given RMS Velocity of Gas?

Temperature of Gas given RMS Velocity of Gas calculator uses Temperature of Gas = Root Mean Square Velocity^2*Molar Mass/(3*[R]) to calculate the Temperature of Gas, The Temperature of Gas given RMS Velocity of Gas formula is a measure of the average translational kinetic energy of the molecules. Temperature of Gas is denoted by T_g symbol.

How to calculate Temperature of Gas given RMS Velocity of Gas using this online calculator? To use this online calculator for Temperature of Gas given RMS Velocity of Gas, enter Root Mean Square Velocity (V_rms) & Molar Mass (M_molar) and hit the calculate button. Here is how the Temperature of Gas given RMS Velocity of Gas calculation can be explained with given input values -> 158.7956 = 300^2*0.04401/(3*[R]).

FAQ

What is Temperature of Gas given RMS Velocity of Gas?

The Temperature of Gas given RMS Velocity of Gas formula is a measure of the average translational kinetic energy of the molecules and is represented as T_g = V_rms^2*M_molar/(3*[R]) or Temperature of Gas = Root Mean Square Velocity^2*Molar Mass/(3*[R]). The Root Mean Square Velocity is the square root of the average of the square of the velocity. As such, it has units of velocity & Molar Mass is the mass of a given substance divided by the amount of substance.

How to calculate Temperature of Gas given RMS Velocity of Gas?

The Temperature of Gas given RMS Velocity of Gas formula is a measure of the average translational kinetic energy of the molecules is calculated using Temperature of Gas = Root Mean Square Velocity^2*Molar Mass/(3*[R]). To calculate Temperature of Gas given RMS Velocity of Gas, you need Root Mean Square Velocity (V_rms) & Molar Mass (M_molar). With our tool, you need to enter the respective value for Root Mean Square Velocity & Molar Mass and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Temperature of Gas?

In this formula, Temperature of Gas uses Root Mean Square Velocity & Molar Mass. We can use 3 other way(s) to calculate the same, which is/are as follows -

Temperature of Gas = (Average Speed of Gas^2)*pi*Molar Mass/(8*[R])
Temperature of Gas = Equipartition Energy*2/[BoltZ]
Temperature of Gas = Most Probable Speed^2*Molar Mass/(2*[R])

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