RMS Speed Calculator

✖The temperature of Gas is the measure of hotness or coldness of a gas.ⓘ Temperature of Gas [T_g]			+10% -10%
✖Molar Mass is the mass of a given substance divided by the amount of substance.ⓘ Molar Mass [M_molar]			+10% -10%

✖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.ⓘ RMS Speed [V_rms]

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Formula

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RMS Speed

Formula

`"V"_{"rms"} = sqrt((3*"[R]"*"T"_{"g"})/"M"_{"molar"})`

Example

`"159.7012m/s"=sqrt((3*"[R]"*"45K")/"44.01g/mol")`

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RMS Speed Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

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.
Temperature of Gas - (Measured in Kelvin) - The temperature of Gas is the measure of hotness or coldness of a gas.
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

Temperature of Gas: 45 Kelvin --> 45 Kelvin 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

V_rms = sqrt((3*[R]*T_g)/M_molar) --> sqrt((3*[R]*45)/0.04401)

Evaluating ... ...

V_rms = 159.701241569226

STEP 3: Convert Result to Output's Unit

159.701241569226 Meter per Second --> No Conversion Required

FINAL ANSWER

159.701241569226 ≈ 159.7012 Meter per Second <-- Root Mean Square Velocity

(Calculation completed in 00.004 seconds)

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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< 13 Factors of Thermodynamics Calculators

Van der Waals Equation

Go Van der Waals Equation = [R]*Temperature/(Molar Volume-Gas Constant b)-Gas Constant a/Molar Volume^2

Average Speed of Gases

Go Average Speed of Gas = sqrt((8*[R]*Temperature of Gas A)/(pi*Molar Mass))

Molar Mass of Gas given Average Speed of Gas

Go Molar Mass = (8*[R]*Temperature of Gas A)/(pi*Average Speed of Gas^2)

RMS Speed

Go Root Mean Square Velocity = sqrt((3*[R]*Temperature of Gas)/Molar Mass)

Most Probable Speed

Go Most Probable Speed = sqrt((2*[R]*Temperature of Gas A)/Molar Mass)

Newton's Law of Cooling

Go Heat Flux = Heat Transfer Coefficient*(Surface Temperature-Temperature of Characteristic Fluid)

Change in Momentum

Go Change in Momentum = Mass of Body*(Initial Velocity at Point 2-Initial Velocity at Point 1)

Input Power to Turbine or Power given to Turbine

Go Power = Density*Acceleration due to Gravity*Discharge*Head

Degree of Freedom given Equipartition Energy

Go Degree of Freedom = 2*Equipartition Energy/([BoltZ]*Temperature of Gas B)

Molar Mass of Gas given RMS Velocity of Gas

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

Molar Mass of Gas given Most Probable Speed of Gas

Go Molar Mass = (2*[R]*Temperature of Gas A)/Most Probable Speed^2

Specific Gas Constant

Go Specific Gas Constant = [R]/Molar Mass

Absolute Humidity

Go Absolute Humidity = Weight/Volume of Gas

RMS Speed Formula

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

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.

How to Calculate RMS Speed?

RMS Speed calculator uses Root Mean Square Velocity = sqrt((3*[R]*Temperature of Gas)/Molar Mass) to calculate the Root Mean Square Velocity, The RMS 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. ... The root-mean-square speed takes into account both molecular weight and temperature, two factors that directly affect the kinetic energy of a material. Root Mean Square Velocity is denoted by V_rms symbol.

How to calculate RMS Speed using this online calculator? To use this online calculator for RMS Speed, enter Temperature of Gas (T_g) & Molar Mass (M_molar) and hit the calculate button. Here is how the RMS Speed calculation can be explained with given input values -> 159.7012 = sqrt((3*[R]*45)/0.04401).

FAQ

What is RMS Speed?

The RMS 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. ... The root-mean-square speed takes into account both molecular weight and temperature, two factors that directly affect the kinetic energy of a material and is represented as V_rms = sqrt((3*[R]*T_g)/M_molar) or Root Mean Square Velocity = sqrt((3*[R]*Temperature of Gas)/Molar Mass). The temperature of Gas is the measure of hotness or coldness of a gas & Molar Mass is the mass of a given substance divided by the amount of substance.

How to calculate RMS Speed?

The RMS 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. ... The root-mean-square speed takes into account both molecular weight and temperature, two factors that directly affect the kinetic energy of a material is calculated using Root Mean Square Velocity = sqrt((3*[R]*Temperature of Gas)/Molar Mass). To calculate RMS Speed, you need Temperature of Gas (T_g) & Molar Mass (M_molar). With our tool, you need to enter the respective value for Temperature of Gas & Molar Mass and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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