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

GoAdiabatic Index of Real Gas Formula

GoAdiabatic Index of Real Gas given Heat Capacity at Constant Volume Formula

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Adiabatic Index is the ratio of the heat capacity at constant pressure (CP) to heat capacity at constant volume (CV). Check FAQs

k = \frac{C p}{C p - (\frac{v \cdot T \cdot (α^{2})}{K T})}

k - Adiabatic Index?C_p - Heat Capacity Constant Pressure?v - Specific Volume?T - Temperature?α - Coefficient of Thermal Expansion?K_T - Isothermal Compressibility?

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

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Here is how the Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure equation looks like with Values.

Here is how the Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure equation looks like with Units.

Here is how the Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure equation looks like.

1.0001 = \frac{1001}{1001 - (\frac{11 \cdot 85 \cdot ({0.1}^{2})}{75})}

1.0001 = \frac{1001J/(kg*K)}{1001J/(kg*K) - (\frac{11m³/kg \cdot 85K \cdot ({0.1K⁻¹}^{2})}{75m²/N})}

1.0001 = \frac{1001}{1001 - (\frac{11 \cdot 85 \cdot ({0.1}^{2})}{75})}

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

Follow our step by step solution on how to calculate Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure?

FIRST Step Consider the formula

k = \frac{C p}{C p - (\frac{v \cdot T \cdot (α^{2})}{K T})}

Next Step Substitute values of Variables

∴

k = \frac{1001J/(kg*K)}{1001J/(kg*K) - (\frac{11m³/kg \cdot 85K \cdot ({0.1K⁻¹}^{2})}{75m²/N})}

Next Step Prepare to Evaluate

∴

k = \frac{1001}{1001 - (\frac{11 \cdot 85 \cdot ({0.1}^{2})}{75})}

Next Step Evaluate

∴

k = 1.00012455763721

LAST Step Rounding Answer

∴

k = 1.0001

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

Variables

Adiabatic Index

Adiabatic Index is the ratio of the heat capacity at constant pressure (CP) to heat capacity at constant volume (CV).

Symbol: k

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Adiabatic Index

Heat Capacity Constant Pressure

Heat capacity constant pressure is the amount of heat energy absorbed/released per unit mass of a substance where the pressure does not change.

Symbol: C_p

Measurement: Specific Heat CapacityUnit: J/(kg*K)

Note: Value should be greater than 0.

Formulas to find Heat Capacity Constant Pressure

Specific Volume

Specific Volume of the body is its volume per unit mass.

Symbol: v

Measurement: Specific VolumeUnit: m³/kg

Note: Value should be greater than 0.

Formulas to find Specific Volume

Temperature

Temperature is the degree or intensity of heat present in a substance or object.

Symbol: T

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Temperature

Coefficient of Thermal Expansion

Coefficient of thermal expansion describes how the size of an object changes with a change in temperature.

Symbol: α

Measurement: Thermal ExpansionUnit: K⁻¹

Note: Value can be positive or negative.

Formulas to find Coefficient of Thermal Expansion

Isothermal Compressibility

The isothermal compressibility is the change in volume due to change in pressure at constant temperature.

Symbol: K_T

Measurement: CompressibilityUnit: m²/N

Note: Value can be positive or negative.

Formulas to find Isothermal Compressibility

Other Formulas to find Adiabatic Index

Go Adiabatic Index of Real Gas

k = \frac{C p}{C v}

Go Adiabatic Index of Real Gas given Heat Capacity at Constant Volume

k = \frac{(\frac{v \cdot T \cdot (α^{2})}{K T}) + C v}{C v}

Other formulas in Specific Heat Capacity category

Go Difference between Cp and Cv of Real Gas

δC pv = \frac{v \cdot T \cdot (α^{2})}{K T}

Go Heat Capacity at Constant Pressure of Real Gas

C p = (\frac{v \cdot T \cdot (α^{2})}{K T}) + C v

Go Heat Capacity at Constant Volume of Real Gas

C v = C p - (\frac{v \cdot T \cdot (α^{2})}{K T})

Go Coefficient of Thermal Expansion of Real Gas

α = \sqrt{\frac{(C p - C v) \cdot K T}{v \cdot T}}

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

Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure evaluator uses Adiabatic Index = Heat Capacity Constant Pressure/(Heat Capacity Constant Pressure-((Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Isothermal Compressibility)) to evaluate 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 evaluate Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure using this online evaluator? To use this online evaluator 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.

FAQs on Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure

What is the formula to find Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure?

The formula of Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure is expressed as Adiabatic Index = Heat Capacity Constant Pressure/(Heat Capacity Constant Pressure-((Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Isothermal Compressibility)). Here is an example- 1.000125 = 1001/(1001-((11*85*(0.1^2))/75)).

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

With Heat Capacity Constant Pressure (C_p), Specific Volume (v), Temperature (T), Coefficient of Thermal Expansion (α) & Isothermal Compressibility (K_T) we can find Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure using the formula - Adiabatic Index = Heat Capacity Constant Pressure/(Heat Capacity Constant Pressure-((Specific Volume*Temperature*(Coefficient of Thermal Expansion^2))/Isothermal Compressibility)).

What are the other ways to Calculate Adiabatic Index?

Here are the different ways to Calculate Adiabatic Index-

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

​GoAdiabatic Index of Real Gas Formula

​GoAdiabatic Index of Real Gas given Heat Capacity at Constant Volume Formula

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

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

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

Other Formulas to find Adiabatic Index

Other formulas in Specific Heat Capacity category

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

FAQs on Adiabatic Index of Real Gas given Heat Capacity at Constant Pressure

Variable Name

GoAdiabatic Index of Real Gas Formula

GoAdiabatic Index of Real Gas given Heat Capacity at Constant Volume Formula