Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure Solution

STEP 0: Pre-Calculation Summary
Formula Used
Adiabatic Index = Heat Capacity Constant Pressure/(Heat Capacity Constant Pressure-((Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Isothermal Compressibility))
k = Cp/(Cp-((v*T*(α^2))/KT))
This formula uses 6 Variables
Variables Used
Adiabatic Index - Adiabatic Index is the ratio of the heat capacity at constant pressure (CP) to heat capacity at constant volume (CV).
Heat Capacity Constant Pressure - (Measured in Joule per Kilogram per K) - Heat capacity constant pressure is the amount of heat energy absorbed/released per unit mass of a substance where the pressure does not change.
Specific Volume - (Measured in Cubic Meter per Kilogram) - Specific Volume of the body is its volume per unit mass.
Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.
Coefficient of Thermal Expansion - (Measured in 1 Per Kelvin) - Coefficient of thermal expansion describes how the size of an object changes with a change in temperature.
Isothermal Compressibility - (Measured in Square Meter per Newton) - The isothermal compressibility is the change in volume due to change in pressure at constant temperature.
STEP 1: Convert Input(s) to Base Unit
Heat Capacity Constant Pressure: 1001 Joule per Kilogram per K --> 1001 Joule per Kilogram per K No Conversion Required
Specific Volume: 11 Cubic Meter per Kilogram --> 11 Cubic Meter per Kilogram No Conversion Required
Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required
Coefficient of Thermal Expansion: 0.1 1 Per Kelvin --> 0.1 1 Per Kelvin No Conversion Required
Isothermal Compressibility: 75 Square Meter per Newton --> 75 Square Meter per Newton No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
k = Cp/(Cp-((v*T*(α^2))/KT)) --> 1001/(1001-((11*85*(0.1^2))/75))
Evaluating ... ...
k = 1.00012455763721
STEP 3: Convert Result to Output's Unit
1.00012455763721 --> No Conversion Required
FINAL ANSWER
1.00012455763721 1.000125 <-- Adiabatic Index
(Calculation completed in 00.004 seconds)

Credits

Creator Image
Created by Prerana Bakli
University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA
Prerana Bakli has created this Calculator and 800+ more calculators!
Verifier Image
Verified by Prashant Singh
K J Somaiya College of science (K J Somaiya), Mumbai
Prashant Singh has verified this Calculator and 500+ more calculators!

Specific Heat Capacity Calculators

Coefficient of Thermal Expansion of Real Gas
​ LaTeX ​ Go Coefficient of Thermal Expansion = sqrt(((Heat Capacity Constant Pressure-Heat Capacity Constant Volume)*Isothermal Compressibility)/(Specific Volume*Temperature))
Heat Capacity at Constant Pressure of Real Gas
​ LaTeX ​ Go Heat Capacity Constant Pressure = ((Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Isothermal Compressibility)+Heat Capacity Constant Volume
Heat Capacity at Constant Volume of Real Gas
​ LaTeX ​ Go Heat Capacity Constant Volume = Heat Capacity Constant Pressure-((Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Isothermal Compressibility)
Difference between Cp and Cv of Real Gas
​ LaTeX ​ Go Difference in Heat Capacities = (Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Isothermal Compressibility

Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure Formula

​LaTeX ​Go
Adiabatic Index = Heat Capacity Constant Pressure/(Heat Capacity Constant Pressure-((Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Isothermal Compressibility))
k = Cp/(Cp-((v*T*(α^2))/KT))

What are postulates of Kinetic molecular theory of gas?

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 Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure?

Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure calculator uses Adiabatic Index = Heat Capacity Constant Pressure/(Heat Capacity Constant Pressure-((Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Isothermal Compressibility)) to calculate the Adiabatic Index, The Adiabatic Index of Real Gas given Heat Capacity at constant Pressure is the ratio of the heat capacity at constant pressure (CP) to heat capacity at constant volume (CV). Adiabatic Index is denoted by k symbol.

How to calculate Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure using this online calculator? To use this online calculator for Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure, enter Heat Capacity Constant Pressure (Cp), Specific Volume (v), Temperature (T), Coefficient of Thermal Expansion (α) & Isothermal Compressibility (KT) and hit the calculate button. Here is how the Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure calculation can be explained with given input values -> 1.000125 = 1001/(1001-((11*85*(0.1^2))/75)).

FAQ

What is Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure?
The Adiabatic Index of Real Gas given Heat Capacity at constant Pressure is the ratio of the heat capacity at constant pressure (CP) to heat capacity at constant volume (CV) and is represented as k = Cp/(Cp-((v*T*(α^2))/KT)) or Adiabatic Index = Heat Capacity Constant Pressure/(Heat Capacity Constant Pressure-((Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Isothermal Compressibility)). Heat capacity constant pressure is the amount of heat energy absorbed/released per unit mass of a substance where the pressure does not change, Specific Volume of the body is its volume per unit mass, Temperature is the degree or intensity of heat present in a substance or object, Coefficient of thermal expansion describes how the size of an object changes with a change in temperature & The isothermal compressibility is the change in volume due to change in pressure at constant temperature.
How to calculate Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure?
The Adiabatic Index of Real Gas given Heat Capacity at constant Pressure is the ratio of the heat capacity at constant pressure (CP) to heat capacity at constant volume (CV) is calculated using Adiabatic Index = Heat Capacity Constant Pressure/(Heat Capacity Constant Pressure-((Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Isothermal Compressibility)). To calculate Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure, you need Heat Capacity Constant Pressure (Cp), Specific Volume (v), Temperature (T), Coefficient of Thermal Expansion (α) & Isothermal Compressibility (KT). With our tool, you need to enter the respective value for Heat Capacity Constant Pressure, Specific Volume, Temperature, Coefficient of Thermal Expansion & Isothermal Compressibility 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 Adiabatic Index?
In this formula, Adiabatic Index uses Heat Capacity Constant Pressure, Specific Volume, Temperature, Coefficient of Thermal Expansion & Isothermal Compressibility. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Adiabatic Index = Heat Capacity Constant Pressure/Heat Capacity Constant Volume
  • Adiabatic Index = (((Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Isothermal Compressibility)+Heat Capacity Constant Volume)/Heat Capacity Constant Volume
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!