Thermal Pressure Coefficient given Compressibility Factors and Cp Calculator

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✖The Isentropic Compressibility is the change in volume due to change in pressure at constant entropy.ⓘ Isentropic Compressibility [K_S]			+10% -10%
✖The isothermal compressibility is the change in volume due to change in pressure at constant temperature.ⓘ Isothermal Compressibility [K_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%
✖Molar Specific Heat Capacity at Constant Pressure 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 pressure.ⓘ Molar Specific Heat Capacity at Constant Pressure [C_p]			+10% -10%
✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature [T]			+10% -10%

✖Coefficient of Thermal Pressure is a measure of the relative pressure change of a fluid or a solid as a response to a temperature change at constant volume.ⓘ Thermal Pressure Coefficient given Compressibility Factors and Cp [Λ_coeff]

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Formula

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Thermal Pressure Coefficient given Compressibility Factors and Cp

Formula

`"Λ"_{"coeff"} = sqrt((((1/"K"_{"S"})-(1/"K"_{"T"}))*"ρ"* ("C"_{"p"}-"[R]"))/"T")`

Example

`"1.126928Pa/K"=sqrt((((1/"70m²/N")-(1/"75m²/N"))*"997kg/m³"* ("122J/K*mol"-"[R]"))/"85K")`

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Thermal Pressure Coefficient given Compressibility Factors and Cp Solution

STEP 0: Pre-Calculation Summary

Formula Used

Coefficient of Thermal Pressure = sqrt((((1/Isentropic Compressibility)-(1/Isothermal Compressibility))*Density* (Molar Specific Heat Capacity at Constant Pressure-[R]))/Temperature)
Λ_coeff = sqrt((((1/K_S)-(1/K_T))*ρ* (C_p-[R]))/T)
This formula uses 1 Constants, 1 Functions, 6 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

Coefficient of Thermal Pressure - (Measured in Pascal per Kelvin) - Coefficient of Thermal Pressure is a measure of the relative pressure change of a fluid or a solid as a response to a temperature change at constant volume.
Isentropic Compressibility - (Measured in Square Meter per Newton) - The Isentropic Compressibility is the change in volume due to change in pressure at constant entropy.
Isothermal Compressibility - (Measured in Square Meter per Newton) - The isothermal compressibility is the change in volume due to change in pressure at constant temperature.
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.
Molar Specific Heat Capacity at Constant Pressure - (Measured in Joule Per Kelvin Per Mole) - Molar Specific Heat Capacity at Constant Pressure 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 pressure.
Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.

STEP 1: Convert Input(s) to Base Unit

Isentropic Compressibility: 70 Square Meter per Newton --> 70 Square Meter per Newton No Conversion Required
Isothermal Compressibility: 75 Square Meter per Newton --> 75 Square Meter per Newton No Conversion Required
Density: 997 Kilogram per Cubic Meter --> 997 Kilogram per Cubic Meter No Conversion Required
Molar Specific Heat Capacity at Constant Pressure: 122 Joule Per Kelvin Per Mole --> 122 Joule Per Kelvin Per Mole No Conversion Required
Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Λ_coeff = sqrt((((1/K_S)-(1/K_T))*ρ* (C_p-[R]))/T) --> sqrt((((1/70)-(1/75))*997* (122-[R]))/85)

Evaluating ... ...

Λ_coeff = 1.12692775770636

STEP 3: Convert Result to Output's Unit

1.12692775770636 Pascal per Kelvin --> No Conversion Required

FINAL ANSWER

1.12692775770636 ≈ 1.126928 Pascal per Kelvin <-- Coefficient of Thermal Pressure

(Calculation completed in 00.004 seconds)

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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)

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)

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)

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

Thermal Pressure Coefficient given Compressibility Factors and Cp Formula

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 Thermal Pressure Coefficient given Compressibility Factors and Cp?

Thermal Pressure Coefficient given Compressibility Factors and Cp calculator uses Coefficient of Thermal Pressure = sqrt((((1/Isentropic Compressibility)-(1/Isothermal Compressibility))*Density* (Molar Specific Heat Capacity at Constant Pressure-[R]))/Temperature) to calculate the Coefficient of Thermal Pressure, The Thermal pressure coefficient given compressibility factors and Cp is a measure of the relative pressure change of a fluid or a solid as a response to a temperature change at constant volume. Coefficient of Thermal Pressure is denoted by Λ_coeff symbol.

How to calculate Thermal Pressure Coefficient given Compressibility Factors and Cp using this online calculator? To use this online calculator for Thermal Pressure Coefficient given Compressibility Factors and Cp, enter Isentropic Compressibility (K_S), Isothermal Compressibility (K_T), Density (ρ), Molar Specific Heat Capacity at Constant Pressure (C_p) & Temperature (T) and hit the calculate button. Here is how the Thermal Pressure Coefficient given Compressibility Factors and Cp calculation can be explained with given input values -> 1.126928 = sqrt((((1/70)-(1/75))*997* (122-[R]))/85).

FAQ

What is Thermal Pressure Coefficient given Compressibility Factors and Cp?

The Thermal pressure coefficient given compressibility factors and Cp is a measure of the relative pressure change of a fluid or a solid as a response to a temperature change at constant volume and is represented as Λ_coeff = sqrt((((1/K_S)-(1/K_T))*ρ* (C_p-[R]))/T) or Coefficient of Thermal Pressure = sqrt((((1/Isentropic Compressibility)-(1/Isothermal Compressibility))*Density* (Molar Specific Heat Capacity at Constant Pressure-[R]))/Temperature). The Isentropic Compressibility is the change in volume due to change in pressure at constant entropy, The isothermal compressibility is the change in volume due to change in pressure at constant temperature, 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, Molar Specific Heat Capacity at Constant Pressure 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 pressure & Temperature is the degree or intensity of heat present in a substance or object.

How to calculate Thermal Pressure Coefficient given Compressibility Factors and Cp?

The Thermal pressure coefficient given compressibility factors and Cp is a measure of the relative pressure change of a fluid or a solid as a response to a temperature change at constant volume is calculated using Coefficient of Thermal Pressure = sqrt((((1/Isentropic Compressibility)-(1/Isothermal Compressibility))*Density* (Molar Specific Heat Capacity at Constant Pressure-[R]))/Temperature). To calculate Thermal Pressure Coefficient given Compressibility Factors and Cp, you need Isentropic Compressibility (K_S), Isothermal Compressibility (K_T), Density (ρ), Molar Specific Heat Capacity at Constant Pressure (C_p) & Temperature (T). With our tool, you need to enter the respective value for Isentropic Compressibility, Isothermal Compressibility, Density, Molar Specific Heat Capacity at Constant Pressure & Temperature 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 Coefficient of Thermal Pressure?

In this formula, Coefficient of Thermal Pressure uses Isentropic Compressibility, Isothermal Compressibility, Density, Molar Specific Heat Capacity at Constant Pressure & Temperature. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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