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Internal Molar Energy of Linear Molecule Formula

GoInternal Molar Energy of Linear Molecule given Atomicity Formula

GoInternal Molar Energy of Non-Linear Molecule given Atomicity Formula

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Molar 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 molar = ((\frac{3}{2}) \cdot [R] \cdot T) + ((0.5 \cdot I y \cdot ({ω y}^{2})) + (0.5 \cdot I z \cdot ({ω z}^{2}))) + ((3 \cdot N) - 5) \cdot ([R] \cdot T)

U_molar - Molar Internal Energy?T - Temperature?I_y - Moment of Inertia along Y-axis?ω_y - Angular Velocity along Y-axis?I_z - Moment of Inertia along Z-axis?ω_z - Angular Velocity along Z-axis?N - Atomicity?[R] - Universal gas constant?[R] - Universal gas constant?

Internal Molar Energy of Linear Molecule Example

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Here is how the Internal Molar Energy of Linear Molecule equation looks like with Values.

Here is how the Internal Molar Energy of Linear Molecule equation looks like with Units.

Here is how the Internal Molar Energy of Linear Molecule equation looks like.

3914.0461 = ((\frac{3}{2}) \cdot 8.3145 \cdot 85) + ((0.5 \cdot 60 \cdot (35^{2})) + (0.5 \cdot 65 \cdot (40^{2}))) + ((3 \cdot 3) - 5) \cdot (8.3145 \cdot 85)

3914.0461J = ((\frac{3}{2}) \cdot 8.3145 \cdot 85K) + ((0.5 \cdot 60kg·m² \cdot ({35degree/s}^{2})) + (0.5 \cdot 65kg·m² \cdot ({40degree/s}^{2}))) + ((3 \cdot 3) - 5) \cdot (8.3145 \cdot 85K)

3914.0461 = ((\frac{3}{2}) \cdot 8.3145 \cdot 85) + ((0.5 \cdot 60 \cdot (35^{2})) + (0.5 \cdot 65 \cdot (40^{2}))) + ((3 \cdot 3) - 5) \cdot (8.3145 \cdot 85)

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Internal Molar Energy of Linear Molecule Solution

Follow our step by step solution on how to calculate Internal Molar Energy of Linear Molecule?

FIRST Step Consider the formula

U molar = ((\frac{3}{2}) \cdot [R] \cdot T) + ((0.5 \cdot I y \cdot ({ω y}^{2})) + (0.5 \cdot I z \cdot ({ω z}^{2}))) + ((3 \cdot N) - 5) \cdot ([R] \cdot T)

Next Step Substitute values of Variables

∴

U molar = ((\frac{3}{2}) \cdot [R] \cdot 85K) + ((0.5 \cdot 60kg·m² \cdot ({35degree/s}^{2})) + (0.5 \cdot 65kg·m² \cdot ({40degree/s}^{2}))) + ((3 \cdot 3) - 5) \cdot ([R] \cdot 85K)

Next Step Substitute values of Constants

∴

U molar = ((\frac{3}{2}) \cdot 8.3145 \cdot 85K) + ((0.5 \cdot 60kg·m² \cdot ({35degree/s}^{2})) + (0.5 \cdot 65kg·m² \cdot ({40degree/s}^{2}))) + ((3 \cdot 3) - 5) \cdot (8.3145 \cdot 85K)

Next Step Convert Units

∴

U molar = ((\frac{3}{2}) \cdot 8.3145 \cdot 85K) + ((0.5 \cdot 60kg·m² \cdot ({0.6109rad/s}^{2})) + (0.5 \cdot 65kg·m² \cdot ({0.6981rad/s}^{2}))) + ((3 \cdot 3) - 5) \cdot (8.3145 \cdot 85K)

Next Step Prepare to Evaluate

∴

U molar = ((\frac{3}{2}) \cdot 8.3145 \cdot 85) + ((0.5 \cdot 60 \cdot ({0.6109}^{2})) + (0.5 \cdot 65 \cdot ({0.6981}^{2}))) + ((3 \cdot 3) - 5) \cdot (8.3145 \cdot 85)

Next Step Evaluate

∴

U molar = 3914.0460699927J

LAST Step Rounding Answer

∴

U molar = 3914.0461J

Internal Molar Energy of Linear Molecule Formula Elements

Variables

Constants

Molar Internal Energy

Molar 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_molar

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Molar Internal Energy

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

Moment of Inertia along Y-axis

The Moment of Inertia along Y-axis of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about Y-axis.

Symbol: I_y

Measurement: Moment of InertiaUnit: kg·m²

Note: Value can be positive or negative.

Formulas to find Moment of Inertia along Y-axis

Angular Velocity along Y-axis

The Angular Velocity along Y-axis also known as angular frequency vector, is a vector measure of rotation rate, that refers to how fast an object rotates or revolves relative to another point.

Symbol: ω_y

Measurement: Angular VelocityUnit: degree/s

Note: Value can be positive or negative.

Formulas to find Angular Velocity along Y-axis

Moment of Inertia along Z-axis

The Moment of Inertia along Z-axis of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about Z-axis.

Symbol: I_z

Measurement: Moment of InertiaUnit: kg·m²

Note: Value can be positive or negative.

Formulas to find Moment of Inertia along Z-axis

Angular Velocity along Z-axis

The Angular Velocity along Z-axis also known as angular frequency vector, is a vector measure of rotation rate, that refers to how fast an object rotates or revolves relative to another point.

Symbol: ω_z

Measurement: Angular VelocityUnit: degree/s

Note: Value can be positive or negative.

Formulas to find Angular Velocity along Z-axis

Atomicity

The Atomicity is defined as the total number of atoms present in a molecule or element.

Symbol: N

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Atomicity

Universal gas constant

Universal gas constant is a fundamental physical constant that appears in the ideal gas law, relating the pressure, volume, and temperature of an ideal gas.

Symbol: [R]

Value: 8.31446261815324

Universal gas constant

Universal gas constant is a fundamental physical constant that appears in the ideal gas law, relating the pressure, volume, and temperature of an ideal gas.

Symbol: [R]

Value: 8.31446261815324

Other Formulas to find Molar Internal Energy

Go Internal Molar Energy of Linear Molecule given Atomicity

U molar = ((6 \cdot N) - 5) \cdot (0.5 \cdot [R] \cdot T)

Go Internal Molar Energy of Non-Linear Molecule given Atomicity

U molar = ((6 \cdot N) - 6) \cdot (0.5 \cdot [R] \cdot T)

Other formulas in Equipartition Principle and Heat Capacity category

Go Average Thermal Energy of Non-linear polyatomic Gas Molecule given Atomicity

Q atomicity = ((6 \cdot N) - 6) \cdot (0.5 \cdot [BoltZ] \cdot T)

Go Average Thermal Energy of Linear Polyatomic Gas Molecule given Atomicity

Q atomicity = ((6 \cdot N) - 5) \cdot (0.5 \cdot [BoltZ] \cdot T)

How to Evaluate Internal Molar Energy of Linear Molecule?

Internal Molar Energy of Linear Molecule evaluator uses Molar Internal Energy = ((3/2)*[R]*Temperature)+((0.5*Moment of Inertia along Y-axis*(Angular Velocity along Y-axis^2))+(0.5*Moment of Inertia along Z-axis*(Angular Velocity along Z-axis^2)))+((3*Atomicity)-5)*([R]*Temperature) to evaluate the Molar Internal Energy, The Internal Molar Energy of Linear Molecule 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. Molar Internal Energy is denoted by U_molar symbol.

How to evaluate Internal Molar Energy of Linear Molecule using this online evaluator? To use this online evaluator for Internal Molar Energy of Linear Molecule, enter Temperature (T), Moment of Inertia along Y-axis (I_y), Angular Velocity along Y-axis (ω_y), Moment of Inertia along Z-axis (I_z), Angular Velocity along Z-axis (ω_z) & Atomicity (N) and hit the calculate button.

FAQs on Internal Molar Energy of Linear Molecule

What is the formula to find Internal Molar Energy of Linear Molecule?

The formula of Internal Molar Energy of Linear Molecule is expressed as Molar Internal Energy = ((3/2)*[R]*Temperature)+((0.5*Moment of Inertia along Y-axis*(Angular Velocity along Y-axis^2))+(0.5*Moment of Inertia along Z-axis*(Angular Velocity along Z-axis^2)))+((3*Atomicity)-5)*([R]*Temperature). Here is an example- 3914.046 = ((3/2)*[R]*85)+((0.5*60*(0.610865238197901^2))+(0.5*65*(0.698131700797601^2)))+((3*3)-5)*([R]*85).

How to calculate Internal Molar Energy of Linear Molecule?

With Temperature (T), Moment of Inertia along Y-axis (I_y), Angular Velocity along Y-axis (ω_y), Moment of Inertia along Z-axis (I_z), Angular Velocity along Z-axis (ω_z) & Atomicity (N) we can find Internal Molar Energy of Linear Molecule using the formula - Molar Internal Energy = ((3/2)*[R]*Temperature)+((0.5*Moment of Inertia along Y-axis*(Angular Velocity along Y-axis^2))+(0.5*Moment of Inertia along Z-axis*(Angular Velocity along Z-axis^2)))+((3*Atomicity)-5)*([R]*Temperature). This formula also uses Universal gas constant, Universal gas constant .

What are the other ways to Calculate Molar Internal Energy?

Here are the different ways to Calculate Molar Internal Energy-

Molar Internal Energy=((6*Atomicity)-5)*(0.5*[R]*Temperature)
Molar Internal Energy=((6*Atomicity)-6)*(0.5*[R]*Temperature)
Molar Internal Energy=((3/2)*[R]*Temperature)+((0.5*Moment of Inertia along Y-axis*(Angular Velocity along Y-axis^2))+(0.5*Moment of Inertia along Z-axis*(Angular Velocity along Z-axis^2))+(0.5*Moment of Inertia along X-axis*(Angular Velocity along X-axis^2)))+((3*Atomicity)-6)*([R]*Temperature)

Can the Internal Molar Energy of Linear Molecule be negative?

Yes, the Internal Molar Energy of Linear Molecule, measured in Energy can be negative.

Which unit is used to measure Internal Molar Energy of Linear Molecule?

Internal Molar Energy of Linear Molecule is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Internal Molar Energy of Linear Molecule can be measured.

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Internal Molar Energy of Linear Molecule Formula

​GoInternal Molar Energy of Linear Molecule given Atomicity Formula

​GoInternal Molar Energy of Non-Linear Molecule given Atomicity Formula

Internal Molar Energy of Linear Molecule Example

Internal Molar Energy of Linear Molecule Solution

Internal Molar Energy of Linear Molecule Formula Elements

Other Formulas to find Molar Internal Energy

Other formulas in Equipartition Principle and Heat Capacity category

How to Evaluate Internal Molar Energy of Linear Molecule?

FAQs on Internal Molar Energy of Linear Molecule

Variable Name

GoInternal Molar Energy of Linear Molecule given Atomicity Formula

GoInternal Molar Energy of Non-Linear Molecule given Atomicity Formula