Isothermal Compressibility given Thermal Pressure Coefficient and Cp Solution

STEP 0: Pre-Calculation Summary
Formula Used
Isothermal Compressibility = 1/((1/Isentropic Compressibility)-(((Thermal Pressure Coefficient^2)*Temperature)/(Density*(Molar Specific Heat Capacity at Constant Pressure-[R]))))
KT = 1/((1/KS)-(((Λ^2)*T)/(ρ*(Cp-[R]))))
This formula uses 1 Constants, 6 Variables
Constants Used
[R] - Universal gas constant Value Taken As 8.31446261815324
Variables Used
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.
Thermal Pressure Coefficient - (Measured in Pascal per Kelvin) - Thermal Pressure Coefficient is a measure of the relative pressure change of a fluid or a solid as a response to a temperature change at constant volume.
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.
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.
STEP 1: Convert Input(s) to Base Unit
Isentropic Compressibility: 70 Square Meter per Newton --> 70 Square Meter per Newton No Conversion Required
Thermal Pressure Coefficient: 0.01 Pascal per Kelvin --> 0.01 Pascal per Kelvin 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
Molar Specific Heat Capacity at Constant Pressure: 122 Joule Per Kelvin Per Mole --> 122 Joule Per Kelvin Per Mole No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
KT = 1/((1/KS)-(((Λ^2)*T)/(ρ*(Cp-[R])))) --> 1/((1/70)-(((0.01^2)*85)/(997*(122-[R]))))
Evaluating ... ...
KT = 70.0003674657854
STEP 3: Convert Result to Output's Unit
70.0003674657854 Square Meter per Newton --> No Conversion Required
FINAL ANSWER
70.0003674657854 70.00037 Square Meter per Newton <-- Isothermal Compressibility
(Calculation completed in 00.004 seconds)

Credits

Created by Prerana Bakli
University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA
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National Institute of Information Technology (NIIT), Neemrana
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7 Isothermal Compressibility Calculators

Isothermal Compressibility given Volumetric Coefficient of Thermal Expansion and Cv
Go Isothermal Compressibility = Isentropic Compressibility+(((Volumetric Coefficient of Thermal Expansion^2)*Temperature)/(Density*(Molar Specific Heat Capacity at Constant Volume+[R])))
Isothermal Compressibility given Thermal Pressure Coefficient and Cp
Go Isothermal Compressibility = 1/((1/Isentropic Compressibility)-(((Thermal Pressure Coefficient^2)*Temperature)/(Density*(Molar Specific Heat Capacity at Constant Pressure-[R]))))
Isothermal Compressibility given Volumetric Coefficient of Thermal Expansion and Cp
Go Isothermal Compressibility = Isentropic Compressibility+(((Volumetric Coefficient of Thermal Expansion^2)*Temperature)/(Density*Molar Specific Heat Capacity at Constant Pressure))
Isothermal Compressibility given Thermal Pressure Coefficient and Cv
Go Isothermal Compressibility = 1/((1/Isentropic Compressibility)-(((Thermal Pressure Coefficient^2)*Temperature)/(Density*Molar Specific Heat Capacity at Constant Volume)))
Isothermal Compressibility given Relative Size of Fluctuations in Particle Density
Go Isothermal Compressibility in KTOG = ((Relative Size of Fluctuations/Volume of Gas))/([BoltZ]*Temperature*(Density^2))
Isothermal Compressibility given Molar Heat Capacity at Constant Pressure and Volume
Go Isothermal Compressibility = (Molar Specific Heat Capacity at Constant Pressure/Molar Specific Heat Capacity at Constant Volume)*Isentropic Compressibility
Isothermal Compressibility given Molar Heat Capacity Ratio
Go Isothermal Compressibility = Ratio of Molar Heat Capacity*Isentropic Compressibility

Isothermal Compressibility given Thermal Pressure Coefficient and Cp Formula

Isothermal Compressibility = 1/((1/Isentropic Compressibility)-(((Thermal Pressure Coefficient^2)*Temperature)/(Density*(Molar Specific Heat Capacity at Constant Pressure-[R]))))
KT = 1/((1/KS)-(((Λ^2)*T)/(ρ*(Cp-[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 Isothermal Compressibility given Thermal Pressure Coefficient and Cp?

Isothermal Compressibility given Thermal Pressure Coefficient and Cp calculator uses Isothermal Compressibility = 1/((1/Isentropic Compressibility)-(((Thermal Pressure Coefficient^2)*Temperature)/(Density*(Molar Specific Heat Capacity at Constant Pressure-[R])))) to calculate the Isothermal Compressibility, The Isothermal compressibility given thermal pressure coefficient and Cp is the change in volume due to change in pressure at constant temperature. Isothermal Compressibility is denoted by KT symbol.

How to calculate Isothermal Compressibility given Thermal Pressure Coefficient and Cp using this online calculator? To use this online calculator for Isothermal Compressibility given Thermal Pressure Coefficient and Cp, enter Isentropic Compressibility (KS), Thermal Pressure Coefficient (Λ), Temperature (T), Density (ρ) & Molar Specific Heat Capacity at Constant Pressure (Cp) and hit the calculate button. Here is how the Isothermal Compressibility given Thermal Pressure Coefficient and Cp calculation can be explained with given input values -> 70.00037 = 1/((1/70)-(((0.01^2)*85)/(997*(122-[R])))).

FAQ

What is Isothermal Compressibility given Thermal Pressure Coefficient and Cp?
The Isothermal compressibility given thermal pressure coefficient and Cp is the change in volume due to change in pressure at constant temperature and is represented as KT = 1/((1/KS)-(((Λ^2)*T)/(ρ*(Cp-[R])))) or Isothermal Compressibility = 1/((1/Isentropic Compressibility)-(((Thermal Pressure Coefficient^2)*Temperature)/(Density*(Molar Specific Heat Capacity at Constant Pressure-[R])))). The Isentropic Compressibility is the change in volume due to change in pressure at constant entropy, Thermal Pressure Coefficient is a measure of the relative pressure change of a fluid or a solid as a response to a temperature change at constant volume, 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 & 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.
How to calculate Isothermal Compressibility given Thermal Pressure Coefficient and Cp?
The Isothermal compressibility given thermal pressure coefficient and Cp is the change in volume due to change in pressure at constant temperature is calculated using Isothermal Compressibility = 1/((1/Isentropic Compressibility)-(((Thermal Pressure Coefficient^2)*Temperature)/(Density*(Molar Specific Heat Capacity at Constant Pressure-[R])))). To calculate Isothermal Compressibility given Thermal Pressure Coefficient and Cp, you need Isentropic Compressibility (KS), Thermal Pressure Coefficient (Λ), Temperature (T), Density (ρ) & Molar Specific Heat Capacity at Constant Pressure (Cp). With our tool, you need to enter the respective value for Isentropic Compressibility, Thermal Pressure Coefficient, Temperature, Density & Molar Specific Heat Capacity at Constant Pressure 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 Isothermal Compressibility?
In this formula, Isothermal Compressibility uses Isentropic Compressibility, Thermal Pressure Coefficient, Temperature, Density & Molar Specific Heat Capacity at Constant Pressure. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • Isothermal Compressibility = Ratio of Molar Heat Capacity*Isentropic Compressibility
  • Isothermal Compressibility = Isentropic Compressibility+(((Volumetric Coefficient of Thermal Expansion^2)*Temperature)/(Density*Molar Specific Heat Capacity at Constant Pressure))
  • Isothermal Compressibility = (Molar Specific Heat Capacity at Constant Pressure/Molar Specific Heat Capacity at Constant Volume)*Isentropic Compressibility
  • Isothermal Compressibility = Isentropic Compressibility+(((Volumetric Coefficient of Thermal Expansion^2)*Temperature)/(Density*(Molar Specific Heat Capacity at Constant Volume+[R])))
  • Isothermal Compressibility = 1/((1/Isentropic Compressibility)-(((Thermal Pressure Coefficient^2)*Temperature)/(Density*Molar Specific Heat Capacity at Constant Volume)))
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