Density given Volumetric Coefficient of Thermal Expansion, Compressibility Factors and Cv Solution

STEP 0: Pre-Calculation Summary
Formula Used
Density = ((Volumetric Coefficient of Thermal Expansion^2)*Temperature)/((Isothermal Compressibility-Isentropic Compressibility)*(Molar Specific Heat Capacity at Constant Volume+[R]))
ρ = ((α^2)*T)/((KT-KS)*(Cv+[R]))
This formula uses 1 Constants, 6 Variables
Constants Used
[R] - Universal gas constant Value Taken As 8.31446261815324 Joule / Kelvin * Mole
Variables Used
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.
Volumetric Coefficient of Thermal Expansion - (Measured in 1 Per Kelvin) - Volumetric coefficient of thermal expansion is the tendency of matter to change its volume in response to a change in temperature.
Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.
Isothermal Compressibility - (Measured in Square Meter per Newton) - The isothermal compressibility is the change in volume due to change in pressure at constant temperature.
Isentropic Compressibility - (Measured in Square Meter per Newton) - The Isentropic Compressibility is the change in volume due to change in pressure at constant entropy.
Molar Specific Heat Capacity at Constant Volume - (Measured in Joule Per Kelvin Per Mole) - Molar Specific Heat Capacity at Constant Volume, of a gas is the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant volume.
STEP 1: Convert Input(s) to Base Unit
Volumetric Coefficient of Thermal Expansion: 0.001 1 Per Kelvin --> 0.001 1 Per Kelvin No Conversion Required
Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required
Isothermal Compressibility: 75 Square Meter per Newton --> 75 Square Meter per Newton No Conversion Required
Isentropic Compressibility: 70 Square Meter per Newton --> 70 Square Meter per Newton No Conversion Required
Molar Specific Heat Capacity at Constant Volume: 103 Joule Per Kelvin Per Mole --> 103 Joule Per Kelvin Per Mole No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ρ = ((α^2)*T)/((KT-KS)*(Cv+[R])) --> ((0.001^2)*85)/((75-70)*(103+[R]))
Evaluating ... ...
ρ = 1.52720496511903E-07
STEP 3: Convert Result to Output's Unit
1.52720496511903E-07 Kilogram per Cubic Meter --> No Conversion Required
FINAL ANSWER
1.52720496511903E-07 Kilogram per Cubic Meter <-- Density
(Calculation completed in 00.015 seconds)

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National Institute of Technology (NIT), Meghalaya
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13 Density of Gas Calculators

Density given Volumetric Coefficient of Thermal Expansion, Compressibility Factors and Cv
Go Density = ((Volumetric Coefficient of Thermal Expansion^2)*Temperature)/((Isothermal Compressibility-Isentropic Compressibility)*(Molar Specific Heat Capacity at Constant Volume+[R]))
Density given Thermal Pressure Coefficient, Compressibility Factors and Cp
Go Density = ((Thermal Pressure Coefficient^2)*Temperature)/(((1/Isentropic Compressibility)-(1/Isothermal Compressibility))*(Molar Specific Heat Capacity at Constant Pressure-[R]))
Density given Volumetric Coefficient of Thermal Expansion, Compressibility Factors and Cp
Go Density = ((Volumetric Coefficient of Thermal Expansion^2)*Temperature)/((Isothermal Compressibility-Isentropic Compressibility)*Molar Specific Heat Capacity at Constant Pressure)
Density given Thermal Pressure Coefficient, Compressibility Factors and Cv
Go Density = ((Thermal Pressure Coefficient^2)*Temperature)/(((1/Isentropic Compressibility)-(1/Isothermal Compressibility))*Molar Specific Heat Capacity at Constant Volume)
Density given Relative Size of Fluctuations in Particle Density
Go Density = sqrt(((Relative Size of Fluctuations/Volume))/([BoltZ]*Isothermal Compressibility*Temperature))
Density of Gas given Average Velocity and Pressure in 2D
Go Density of Gas = (pi*Pressure of Gas)/(2*((Average Velocity of Gas)^2))
Density of Gas given Average Velocity and Pressure
Go Density of Gas = (8*Pressure of Gas)/(pi*((Average Velocity of Gas)^2))
Density of Gas given Root Mean Square Speed and Pressure in 2D
Go Density of Gas = (2*Pressure of Gas)/((Root Mean Square Speed)^2)
Density of Gas given Root Mean Square Speed and Pressure
Go Density of Gas = (3*Pressure of Gas)/((Root Mean Square Speed)^2)
Density of Gas given Most Probable Speed Pressure
Go Density of Gas = (2*Pressure of Gas)/((Most Probable Velocity)^2)
Density of Gas given Root Mean Square Speed and Pressure in 1D
Go Density of Gas = (Pressure of Gas)/((Root Mean Square Speed)^2)
Density of Gas given Most Probable Speed Pressure in 2D
Go Density of Gas = (Pressure of Gas)/((Most Probable Velocity)^2)
Density of Material given Isentropic Compressibility
Go Density = 1/(Isentropic Compressibility*(Speed of Sound^2))

Density given Volumetric Coefficient of Thermal Expansion, Compressibility Factors and Cv Formula

Density = ((Volumetric Coefficient of Thermal Expansion^2)*Temperature)/((Isothermal Compressibility-Isentropic Compressibility)*(Molar Specific Heat Capacity at Constant Volume+[R]))
ρ = ((α^2)*T)/((KT-KS)*(Cv+[R]))

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 Density given Volumetric Coefficient of Thermal Expansion, Compressibility Factors and Cv?

Density given Volumetric Coefficient of Thermal Expansion, Compressibility Factors and Cv calculator uses Density = ((Volumetric Coefficient of Thermal Expansion^2)*Temperature)/((Isothermal Compressibility-Isentropic Compressibility)*(Molar Specific Heat Capacity at Constant Volume+[R])) to calculate the Density, The Density given volumetric coefficient of thermal expansion, compressibility factors and Cv is defined as material mass per unit volume and designated by the symbol ρ (rho). Density is denoted by ρ symbol.

How to calculate Density given Volumetric Coefficient of Thermal Expansion, Compressibility Factors and Cv using this online calculator? To use this online calculator for Density given Volumetric Coefficient of Thermal Expansion, Compressibility Factors and Cv, enter Volumetric Coefficient of Thermal Expansion (α), Temperature (T), Isothermal Compressibility (KT), Isentropic Compressibility (KS) & Molar Specific Heat Capacity at Constant Volume (Cv) and hit the calculate button. Here is how the Density given Volumetric Coefficient of Thermal Expansion, Compressibility Factors and Cv calculation can be explained with given input values -> 1.5E-7 = ((0.001^2)*85)/((75-70)*(103+[R])).

FAQ

What is Density given Volumetric Coefficient of Thermal Expansion, Compressibility Factors and Cv?
The Density given volumetric coefficient of thermal expansion, compressibility factors and Cv is defined as material mass per unit volume and designated by the symbol ρ (rho) and is represented as ρ = ((α^2)*T)/((KT-KS)*(Cv+[R])) or Density = ((Volumetric Coefficient of Thermal Expansion^2)*Temperature)/((Isothermal Compressibility-Isentropic Compressibility)*(Molar Specific Heat Capacity at Constant Volume+[R])). Volumetric coefficient of thermal expansion is the tendency of matter to change its volume in response to a change in temperature, Temperature is the degree or intensity of heat present in a substance or object, The isothermal compressibility is the change in volume due to change in pressure at constant temperature, The Isentropic Compressibility is the change in volume due to change in pressure at constant entropy & Molar Specific Heat Capacity at Constant Volume, of a gas is the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant volume.
How to calculate Density given Volumetric Coefficient of Thermal Expansion, Compressibility Factors and Cv?
The Density given volumetric coefficient of thermal expansion, compressibility factors and Cv is defined as material mass per unit volume and designated by the symbol ρ (rho) is calculated using Density = ((Volumetric Coefficient of Thermal Expansion^2)*Temperature)/((Isothermal Compressibility-Isentropic Compressibility)*(Molar Specific Heat Capacity at Constant Volume+[R])). To calculate Density given Volumetric Coefficient of Thermal Expansion, Compressibility Factors and Cv, you need Volumetric Coefficient of Thermal Expansion (α), Temperature (T), Isothermal Compressibility (KT), Isentropic Compressibility (KS) & Molar Specific Heat Capacity at Constant Volume (Cv). With our tool, you need to enter the respective value for Volumetric Coefficient of Thermal Expansion, Temperature, Isothermal Compressibility, Isentropic Compressibility & Molar Specific Heat Capacity at Constant Volume 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 Density?
In this formula, Density uses Volumetric Coefficient of Thermal Expansion, Temperature, Isothermal Compressibility, Isentropic Compressibility & Molar Specific Heat Capacity at Constant Volume. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • Density = 1/(Isentropic Compressibility*(Speed of Sound^2))
  • Density = ((Volumetric Coefficient of Thermal Expansion^2)*Temperature)/((Isothermal Compressibility-Isentropic Compressibility)*Molar Specific Heat Capacity at Constant Pressure)
  • Density = ((Thermal Pressure Coefficient^2)*Temperature)/(((1/Isentropic Compressibility)-(1/Isothermal Compressibility))*(Molar Specific Heat Capacity at Constant Pressure-[R]))
  • Density = ((Thermal Pressure Coefficient^2)*Temperature)/(((1/Isentropic Compressibility)-(1/Isothermal Compressibility))*Molar Specific Heat Capacity at Constant Volume)
  • Density = sqrt(((Relative Size of Fluctuations/Volume))/([BoltZ]*Isothermal Compressibility*Temperature))
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