Relative Size of Fluctuations in Particle Density Calculator

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✖The isothermal compressibility is the change in volume due to change in pressure at constant temperature.ⓘ Isothermal Compressibility [K_T]			+10% -10%
✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature [T]			+10% -10%
✖The Density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object.ⓘ Density [ρ]			+10% -10%
✖The volume of Gas is the amount of space that it occupies.ⓘ Volume of Gas [V]			+10% -10%

✖Relative size of fluctuation gives the variance (mean square deviation) of the particles.ⓘ Relative Size of Fluctuations in Particle Density [ΔNr²]

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Formula

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Relative Size of Fluctuations in Particle Density

Formula

`"ΔNr"^{"2"} = "K"_{"T"}*"[BoltZ]"*"T"*("ρ"^2)*"V"`

Example

`"2E^-15"="75m²/N"*"[BoltZ]"*"85K"*(("997kg/m³")^2)*"22.4L"`

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Download Important Calculator of Compressibility Formulas PDF

Relative Size of Fluctuations in Particle Density Solution

STEP 0: Pre-Calculation Summary

Formula Used

Relative Size of Fluctuation = Isothermal Compressibility*[BoltZ]*Temperature*(Density^2)*Volume of Gas
ΔNr² = K_T*[BoltZ]*T*(ρ^2)*V
This formula uses 1 Constants, 5 Variables

Constants Used

[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23

Variables Used

Relative Size of Fluctuation - Relative size of fluctuation gives the variance (mean square deviation) of the particles.
Isothermal Compressibility - (Measured in Square Meter per Newton) - The isothermal compressibility is the change in volume due to change in pressure at constant temperature.
Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.
Density - (Measured in Kilogram per Cubic Meter) - The Density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object.
Volume of Gas - (Measured in Cubic Meter) - The volume of Gas is the amount of space that it occupies.

STEP 1: Convert Input(s) to Base Unit

Isothermal Compressibility: 75 Square Meter per Newton --> 75 Square Meter per Newton No Conversion Required
Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required
Density: 997 Kilogram per Cubic Meter --> 997 Kilogram per Cubic Meter No Conversion Required
Volume of Gas: 22.4 Liter --> 0.0224 Cubic Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ΔNr² = K_T*[BoltZ]*T*(ρ^2)*V --> 75*[BoltZ]*85*(997^2)*0.0224

Evaluating ... ...

ΔNr² = 1.95975443413542E-15

STEP 3: Convert Result to Output's Unit

1.95975443413542E-15 --> No Conversion Required

FINAL ANSWER

1.95975443413542E-15 ≈ 2E-15 <-- Relative Size of Fluctuation

(Calculation completed in 00.020 seconds)

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Home » Chemistry » Kinetic Theory of Gases » Compressibility » Important Calculator of Compressibility » Relative Size of Fluctuations in Particle Density

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Temperature given Coefficient of Thermal Expansion, Compressibility Factors and Cv

Go Temperature given Coefficient of Thermal Expansion = ((Isothermal Compressibility-Isentropic Compressibility)*Density*(Molar Specific Heat Capacity at Constant Volume+[R]))/(Volumetric Coefficient of Thermal Expansion^2)

Volumetric Coefficient of Thermal Expansion given Compressibility Factors and Cv

Go Volumetric Coefficient of Compressibility = sqrt(((Isothermal Compressibility-Isentropic Compressibility)*Density*(Molar Specific Heat Capacity at Constant Volume+[R]))/Temperature)

Thermal Pressure Coefficient given Compressibility Factors and Cp

Go Coefficient of Thermal Pressure = sqrt((((1/Isentropic Compressibility)-(1/Isothermal Compressibility))*Density*(Molar Specific Heat Capacity at Constant Pressure-[R]))/Temperature)

Temperature given Thermal Pressure Coefficient, Compressibility Factors and Cp

Go Temperature given Cp = (((1/Isentropic Compressibility)-(1/Isothermal Compressibility))*Density*(Molar Specific Heat Capacity at Constant Pressure-[R]))/(Thermal Pressure Coefficient^2)

Temperature given Coefficient of Thermal Expansion, Compressibility Factors and Cp

Go Temperature given Coefficient of Thermal Expansion = ((Isothermal Compressibility-Isentropic Compressibility)*Density*Molar Specific Heat Capacity at Constant Pressure)/(Volumetric Coefficient of Thermal Expansion^2)

Volumetric Coefficient of Thermal Expansion given Compressibility Factors and Cp

Go Volumetric Coefficient of Compressibility = sqrt(((Isothermal Compressibility-Isentropic Compressibility)*Density*Molar Specific Heat Capacity at Constant Pressure)/Temperature)

Thermal Pressure Coefficient given Compressibility Factors and Cv

Go Coefficient of Thermal Pressure = sqrt((((1/Isentropic Compressibility)-(1/Isothermal Compressibility))*Density*Molar Specific Heat Capacity at Constant Volume)/Temperature)

Temperature given Thermal Pressure Coefficient, Compressibility Factors and Cv

Go Temperature given Cv = (((1/Isentropic Compressibility)-(1/Isothermal Compressibility))*Density*Molar Specific Heat Capacity at Constant Volume)/(Thermal Pressure Coefficient^2)

Temperature given Relative Size of Fluctuations in Particle Density

Go Temperature given fluctuations = ((Relative Size of Fluctuations/Volume of Gas))/([BoltZ]*Isothermal Compressibility*(Density^2))

Volume given Relative Size of Fluctuations in Particle Density

Go Volume of Gas given fluctuation size = Relative Size of Fluctuations/(Isothermal Compressibility*[BoltZ]*Temperature*(Density^2))

Relative Size of Fluctuations in Particle Density

Go Relative Size of Fluctuation = Isothermal Compressibility*[BoltZ]*Temperature*(Density^2)*Volume of Gas

Compressibility Factor given Molar Volume of Gases

Go Compressibility Factor for KTOG = Molar Volume of Real Gas/Molar Volume of Ideal Gas

Molar Volume of Real Gas given Compressibility Factor

Go Molar Volume of Gas = Compressibility Factor*Molar Volume of Ideal Gas

Relative Size of Fluctuations in Particle Density Formula

Relative Size of Fluctuation = Isothermal Compressibility*[BoltZ]*Temperature*(Density^2)*Volume of Gas
ΔNr² = K_T*[BoltZ]*T*(ρ^2)*V

What are the postulates of kinetic theory of gases?

1) Actual volume of gas molecules is negligible in comparison to the total volume of the gas. 2) no force of attraction between the gas molecules. 3) Particles of gas are in constant random motion. 4) Particles of gas collide with each other and with the walls of the container. 5)Collisions are perfectly elastic. 6) Different particles of the gas, have different speeds. 7) The average kinetic energy of the gas molecule is directly proportional to the absolute temperature.

How to Calculate Relative Size of Fluctuations in Particle Density?

Relative Size of Fluctuations in Particle Density calculator uses Relative Size of Fluctuation = Isothermal Compressibility*[BoltZ]*Temperature*(Density^2)*Volume of Gas to calculate the Relative Size of Fluctuation, The Relative size of fluctuations in particle density gives the variance (mean square deviation) of the particles. Relative Size of Fluctuation is denoted by ΔNr² symbol.

How to calculate Relative Size of Fluctuations in Particle Density using this online calculator? To use this online calculator for Relative Size of Fluctuations in Particle Density, enter Isothermal Compressibility (K_T), Temperature (T), Density (ρ) & Volume of Gas (V) and hit the calculate button. Here is how the Relative Size of Fluctuations in Particle Density calculation can be explained with given input values -> 2E-15 = 75*[BoltZ]*85*(997^2)*0.0224.

FAQ

What is Relative Size of Fluctuations in Particle Density?

The Relative size of fluctuations in particle density gives the variance (mean square deviation) of the particles and is represented as ΔNr² = K_T*[BoltZ]*T*(ρ^2)*V or Relative Size of Fluctuation = Isothermal Compressibility*[BoltZ]*Temperature*(Density^2)*Volume of Gas. The isothermal compressibility is the change in volume due to change in pressure at constant temperature, Temperature is the degree or intensity of heat present in a substance or object, The Density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object & The volume of Gas is the amount of space that it occupies.

How to calculate Relative Size of Fluctuations in Particle Density?

The Relative size of fluctuations in particle density gives the variance (mean square deviation) of the particles is calculated using Relative Size of Fluctuation = Isothermal Compressibility*[BoltZ]*Temperature*(Density^2)*Volume of Gas. To calculate Relative Size of Fluctuations in Particle Density, you need Isothermal Compressibility (K_T), Temperature (T), Density (ρ) & Volume of Gas (V). With our tool, you need to enter the respective value for Isothermal Compressibility, Temperature, Density & Volume of Gas 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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