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

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Specific Heat Capacity

Berthelot and Modified Berthelot Model of Real Gas

Clausius Model of Real Gas

Peng Robinson Model of Real Gas

Redlich Kwong Model of Real Gas

Saturation Vapour Pressure

Van der Waals Force

Wohl Model of Real Gas

✖Heat capacity constant pressure is the amount of heat energy absorbed/released per unit mass of a substance where the pressure does not change.ⓘ Heat Capacity Constant Pressure [C_p]			+10% -10%
✖Specific Volume of the body is its volume per unit mass.ⓘ Specific Volume [v]			+10% -10%
✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature [T]			+10% -10%
✖Coefficient of thermal expansion describes how the size of an object changes with a change in temperature.ⓘ Coefficient of Thermal Expansion [α]			+10% -10%
✖The isothermal compressibility is the change in volume due to change in pressure at constant temperature.ⓘ Isothermal Compressibility [K_T]			+10% -10%

✖Adiabatic Index is the ratio of the heat capacity at constant pressure (CP) to heat capacity at constant volume (CV).ⓘ Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure [k]

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Formula

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Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure

Formula

`"k" = "C"_{"p"}/("C"_{"p"}-(("v"*"T"*("α"^2))/"K"_{"T"}))`

Example

`"1.000125"="1001J/(kg*K)"/("1001J/(kg*K)"-(("11m³/kg"*"85K"*(("0.1K⁻¹")^2))/"75m²/N"))`

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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 = C_p/(C_p-((v*T*(α^2))/K_T))
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 = C_p/(C_p-((v*T*(α^2))/K_T)) --> 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 00.021 seconds)

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< 14 Specific Heat Capacity Calculators

Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure

Go Adiabatic Index = Heat Capacity Constant Pressure/(Heat Capacity Constant Pressure-((Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Isothermal Compressibility))

Adiabatic Index of Real Gas given Heat Capacity at Constant Volume

Go Adiabatic Index = (((Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Isothermal Compressibility)+Heat Capacity Constant Volume)/Heat Capacity Constant Volume

Coefficient of Thermal Expansion of Real Gas

Go Coefficient of Thermal Expansion = sqrt(((Heat Capacity Constant Pressure-Heat Capacity Constant Volume)*Isothermal Compressibility)/(Specific Volume*Temperature))

Specific Volume of Real Gas given Heat Capacities

Go Specific Volume = ((Heat Capacity Constant Pressure-Heat Capacity Constant Volume)*Isothermal Compressibility)/(Temperature*(Coefficient of Thermal Expansion^2))

Temperature of Real Gas given Heat Capacities

Go Temperature = ((Heat Capacity Constant Pressure-Heat Capacity Constant Volume)*Isothermal Compressibility)/(Specific Volume*(Coefficient of Thermal Expansion^2))

Heat Capacity at Constant Pressure of Real Gas

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

Go Heat Capacity Constant Volume = Heat Capacity Constant Pressure-((Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Isothermal Compressibility)

Isothermal Compressibility of Real Gas

Go Isothermal Compressibility = (Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/(Heat Capacity Constant Pressure-Heat Capacity Constant Volume)

Coefficient of Thermal Expansion of Real Gas given Difference between Cp and Cv

Go Coefficient of Thermal Expansion = sqrt((Difference in Heat Capacities*Isothermal Compressibility)/(Specific Volume*Temperature))

Specific Volume of Real Gas given Difference between Cp and Cv

Go Specific Volume = (Difference in Heat Capacities *Isothermal Compressibility)/(Temperature*(Coefficient of Thermal Expansion^2))

Temperature of Real Gas given Difference between Cp and Cv

Go Temperature = (Difference in Heat Capacities*Isothermal Compressibility)/(Specific Volume*(Coefficient of Thermal Expansion^2))

Isothermal Compressibility of Real Gas given Difference between Cp and Cv

Go Isothermal Compressibility = (Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Difference in Heat Capacities

Difference between Cp and Cv of Real Gas

Go Difference in Heat Capacities = (Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Isothermal Compressibility

Adiabatic Index of Real Gas

Go Adiabatic Index = Heat Capacity Constant Pressure/Heat Capacity Constant Volume

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

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 (C_p), Specific Volume (v), Temperature (T), Coefficient of Thermal Expansion (α) & Isothermal Compressibility (K_T) 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 = C_p/(C_p-((v*T*(α^2))/K_T)) 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 (C_p), Specific Volume (v), Temperature (T), Coefficient of Thermal Expansion (α) & Isothermal Compressibility (K_T). 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

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