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Temperature of Real Gas given Heat Capacities Formula

GoTemperature of Real Gas given Difference between Cp and Cv Formula

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

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

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

Temperature of Real Gas given Heat Capacities Example

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Here is how the Temperature of Real Gas given Heat Capacities equation looks like with Values.

Here is how the Temperature of Real Gas given Heat Capacities equation looks like with Units.

Here is how the Temperature of Real Gas given Heat Capacities equation looks like.

192954.5455 = \frac{(1001 - 718) \cdot 75}{11 \cdot ({0.1}^{2})}

192954.5455K = \frac{(1001J/(kg*K) - 718J/(kg*K)) \cdot 75m²/N}{11m³/kg \cdot ({0.1K⁻¹}^{2})}

192954.5455 = \frac{(1001 - 718) \cdot 75}{11 \cdot ({0.1}^{2})}

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Temperature of Real Gas given Heat Capacities Solution

Follow our step by step solution on how to calculate Temperature of Real Gas given Heat Capacities?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

T = \frac{(1001J/(kg*K) - 718J/(kg*K)) \cdot 75m²/N}{11m³/kg \cdot ({0.1K⁻¹}^{2})}

Next Step Prepare to Evaluate

∴

T = \frac{(1001 - 718) \cdot 75}{11 \cdot ({0.1}^{2})}

Next Step Evaluate

∴

T = 192954.545454545K

LAST Step Rounding Answer

∴

T = 192954.5455K

Temperature of Real Gas given Heat Capacities Formula Elements

Variables

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

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

Heat Capacity Constant Volume

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

Symbol: C_v

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

Note: Value should be greater than 0.

Formulas to find Heat Capacity Constant Volume

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

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

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

Other Formulas to find Temperature

Go Temperature of Real Gas given Difference between Cp and Cv

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

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 Temperature of Real Gas given Heat Capacities?

Temperature of Real Gas given Heat Capacities evaluator uses Temperature = ((Heat Capacity Constant Pressure-Heat Capacity Constant Volume)*Isothermal Compressibility)/(Specific Volume*(Coefficient of Thermal Expansion^2)) to evaluate the Temperature, The Temperature of real gas given Heat Capacities is the degree or intensity of heat present in a substance or object, especially as expressed according to a comparative scale. Temperature is denoted by T symbol.

How to evaluate Temperature of Real Gas given Heat Capacities using this online evaluator? To use this online evaluator for Temperature of Real Gas given Heat Capacities, enter Heat Capacity Constant Pressure (C_p), Heat Capacity Constant Volume (C_v), Isothermal Compressibility (K_T), Specific Volume (v) & Coefficient of Thermal Expansion (α) and hit the calculate button.

FAQs on Temperature of Real Gas given Heat Capacities

What is the formula to find Temperature of Real Gas given Heat Capacities?

The formula of Temperature of Real Gas given Heat Capacities is expressed as Temperature = ((Heat Capacity Constant Pressure-Heat Capacity Constant Volume)*Isothermal Compressibility)/(Specific Volume*(Coefficient of Thermal Expansion^2)). Here is an example- 192954.5 = ((1001-718)*75)/(11*(0.1^2)).

How to calculate Temperature of Real Gas given Heat Capacities?

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

What are the other ways to Calculate Temperature?

Here are the different ways to Calculate Temperature-

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

Can the Temperature of Real Gas given Heat Capacities be negative?

Yes, the Temperature of Real Gas given Heat Capacities, measured in Temperature can be negative.

Which unit is used to measure Temperature of Real Gas given Heat Capacities?

Temperature of Real Gas given Heat Capacities is usually measured using the Kelvin[K] for Temperature. Celsius[K], Fahrenheit[K], Rankine[K] are the few other units in which Temperature of Real Gas given Heat Capacities can be measured.

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Temperature of Real Gas given Heat Capacities Formula

​GoTemperature of Real Gas given Difference between Cp and Cv Formula

Temperature of Real Gas given Heat Capacities Example

Temperature of Real Gas given Heat Capacities Solution

Temperature of Real Gas given Heat Capacities Formula Elements

Other Formulas to find Temperature

Other formulas in Specific Heat Capacity category

How to Evaluate Temperature of Real Gas given Heat Capacities?

FAQs on Temperature of Real Gas given Heat Capacities

Variable Name

GoTemperature of Real Gas given Difference between Cp and Cv Formula