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Molar Internal Energy of Ideal Gas given Boltzmann Constant Formula

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The internal energy of a thermodynamic system is the energy contained within it. It is the energy necessary to create or prepare the system in any given internal state. Check FAQs

U = \frac{F \cdot N moles \cdot [BoltZ] \cdot T g}{2}

U - Internal Energy?F - Degree of Freedom?N_moles - Number of Moles?T_g - Temperature of Gas?[BoltZ] - Boltzmann constant?

Molar Internal Energy of Ideal Gas given Boltzmann Constant Example

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Here is how the Molar Internal Energy of Ideal Gas given Boltzmann Constant equation looks like with Values.

Here is how the Molar Internal Energy of Ideal Gas given Boltzmann Constant equation looks like with Units.

Here is how the Molar Internal Energy of Ideal Gas given Boltzmann Constant equation looks like.

2.5E-20 = \frac{3 \cdot 4 \cdot 1.4E-23 \cdot 300}{2}

2.5E-20J = \frac{3 \cdot 4 \cdot 1.4E-23J/K \cdot 300K}{2}

2.5E-20 = \frac{3 \cdot 4 \cdot 1.4E-23 \cdot 300}{2}

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Molar Internal Energy of Ideal Gas given Boltzmann Constant Solution

Follow our step by step solution on how to calculate Molar Internal Energy of Ideal Gas given Boltzmann Constant?

FIRST Step Consider the formula

U = \frac{F \cdot N moles \cdot [BoltZ] \cdot T g}{2}

Next Step Substitute values of Variables

∴

U = \frac{3 \cdot 4 \cdot [BoltZ] \cdot 300K}{2}

Next Step Substitute values of Constants

∴

U = \frac{3 \cdot 4 \cdot 1.4E-23J/K \cdot 300K}{2}

Next Step Prepare to Evaluate

∴

U = \frac{3 \cdot 4 \cdot 1.4E-23 \cdot 300}{2}

Next Step Evaluate

∴

U = 2.485167336E-20J

LAST Step Rounding Answer

∴

U = 2.5E-20J

Molar Internal Energy of Ideal Gas given Boltzmann Constant Formula Elements

Variables

Constants

Internal Energy

The internal energy of a thermodynamic system is the energy contained within it. It is the energy necessary to create or prepare the system in any given internal state.

Symbol: U

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Internal Energy

Degree of Freedom

The Degree of Freedom of a system is the number of parameters of the system that may vary independently.

Symbol: F

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Degree of Freedom

Number of Moles

Number of Moles is the amount of gas present in moles. 1 mole of gas weighs as much as its molecular weight.

Symbol: N_moles

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Moles

Temperature of Gas

Temperature of Gas is the measure of hotness or coldness of a gas.

Symbol: T_g

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Temperature of Gas

Boltzmann constant

Boltzmann constant relates the average kinetic energy of particles in a gas with the temperature of the gas and is a fundamental constant in statistical mechanics and thermodynamics.

Symbol: [BoltZ]

Value: 1.38064852E-23 J/K

Other formulas in Ideal Gas category

Go Degree of Freedom given Molar Internal Energy of Ideal Gas

F = 2 \cdot \frac{U}{N moles \cdot [R] \cdot T g}

Go Ideal Gas Law for Calculating Pressure

P ideal = [R] \cdot \frac{T g}{V Total}

Go Ideal Gas Law for Calculating Volume

V ideal = [R] \cdot \frac{T g}{P}

Go Isothermal Compression of Ideal Gas

W Iso T = N moles \cdot [R] \cdot T g \cdot 2.303 \cdot \log 10 (\frac{V f}{V i})

How to Evaluate Molar Internal Energy of Ideal Gas given Boltzmann Constant?

Molar Internal Energy of Ideal Gas given Boltzmann Constant evaluator uses Internal Energy = (Degree of Freedom*Number of Moles*[BoltZ]*Temperature of Gas)/2 to evaluate the Internal Energy, Molar Internal Energy of Ideal Gas given Boltzmann Constant is defined as the energy associated with the random, disordered motion of molecules. It is separated in scale from the macroscopic ordered energy associated with moving objects. Internal Energy is denoted by U symbol.

How to evaluate Molar Internal Energy of Ideal Gas given Boltzmann Constant using this online evaluator? To use this online evaluator for Molar Internal Energy of Ideal Gas given Boltzmann Constant, enter Degree of Freedom (F), Number of Moles (N_moles) & Temperature of Gas (T_g) and hit the calculate button.

FAQs on Molar Internal Energy of Ideal Gas given Boltzmann Constant

What is the formula to find Molar Internal Energy of Ideal Gas given Boltzmann Constant?

The formula of Molar Internal Energy of Ideal Gas given Boltzmann Constant is expressed as Internal Energy = (Degree of Freedom*Number of Moles*[BoltZ]*Temperature of Gas)/2. Here is an example- 2.5E-20 = (3*4*[BoltZ]*300)/2.

How to calculate Molar Internal Energy of Ideal Gas given Boltzmann Constant?

With Degree of Freedom (F), Number of Moles (N_moles) & Temperature of Gas (T_g) we can find Molar Internal Energy of Ideal Gas given Boltzmann Constant using the formula - Internal Energy = (Degree of Freedom*Number of Moles*[BoltZ]*Temperature of Gas)/2. This formula also uses Boltzmann constant .

Can the Molar Internal Energy of Ideal Gas given Boltzmann Constant be negative?

Yes, the Molar Internal Energy of Ideal Gas given Boltzmann Constant, measured in Energy can be negative.

Which unit is used to measure Molar Internal Energy of Ideal Gas given Boltzmann Constant?

Molar Internal Energy of Ideal Gas given Boltzmann Constant is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Molar Internal Energy of Ideal Gas given Boltzmann Constant can be measured.

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