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Internal Molar Energy of Non-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})) + (0.5 \cdot I x \cdot ({ω x}^{2}))) + ((3 \cdot N) - 6) \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?I_x - Moment of Inertia along X-axis?ω_x - Angular Velocity along X-axis?N - Atomicity?[R] - Universal gas constant?[R] - Universal gas constant?

Internal Molar Energy of Non-Linear Molecule Example

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

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

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

3214.856 = ((\frac{3}{2}) \cdot 8.3145 \cdot 85) + ((0.5 \cdot 60 \cdot (35^{2})) + (0.5 \cdot 65 \cdot (40^{2})) + (0.5 \cdot 55 \cdot (30^{2}))) + ((3 \cdot 3) - 6) \cdot (8.3145 \cdot 85)

3214.856J = ((\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})) + (0.5 \cdot 55kg·m² \cdot ({30degree/s}^{2}))) + ((3 \cdot 3) - 6) \cdot (8.3145 \cdot 85K)

3214.856 = ((\frac{3}{2}) \cdot 8.3145 \cdot 85) + ((0.5 \cdot 60 \cdot (35^{2})) + (0.5 \cdot 65 \cdot (40^{2})) + (0.5 \cdot 55 \cdot (30^{2}))) + ((3 \cdot 3) - 6) \cdot (8.3145 \cdot 85)

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Internal Molar Energy of Non-Linear Molecule Solution

Follow our step by step solution on how to calculate Internal Molar Energy of Non-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})) + (0.5 \cdot I x \cdot ({ω x}^{2}))) + ((3 \cdot N) - 6) \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})) + (0.5 \cdot 55kg·m² \cdot ({30degree/s}^{2}))) + ((3 \cdot 3) - 6) \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})) + (0.5 \cdot 55kg·m² \cdot ({30degree/s}^{2}))) + ((3 \cdot 3) - 6) \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})) + (0.5 \cdot 55kg·m² \cdot ({0.5236rad/s}^{2}))) + ((3 \cdot 3) - 6) \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})) + (0.5 \cdot 55 \cdot ({0.5236}^{2}))) + ((3 \cdot 3) - 6) \cdot (8.3145 \cdot 85)

Next Step Evaluate

∴

U molar = 3214.85602858939J

LAST Step Rounding Answer

∴

U molar = 3214.856J

Internal Molar Energy of Non-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

Moment of Inertia along X-axis

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

Symbol: I_x

Measurement: Moment of InertiaUnit: kg·m²

Note: Value can be positive or negative.

Formulas to find Moment of Inertia along X-axis

Angular Velocity along X-axis

The Angular Velocity along X-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_x

Measurement: Angular VelocityUnit: degree/s

Note: Value can be positive or negative.

Formulas to find Angular Velocity along X-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 Non-Linear Molecule?

Internal Molar Energy of Non-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))+(0.5*Moment of Inertia along X-axis*(Angular Velocity along X-axis^2)))+((3*Atomicity)-6)*([R]*Temperature) to evaluate the Molar Internal Energy, The Internal Molar Energy of Non-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 Non-Linear Molecule using this online evaluator? To use this online evaluator for Internal Molar Energy of Non-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), Moment of Inertia along X-axis (I_x), Angular Velocity along X-axis (ω_x) & Atomicity (N) and hit the calculate button.

FAQs on Internal Molar Energy of Non-Linear Molecule

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

The formula of Internal Molar Energy of Non-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))+(0.5*Moment of Inertia along X-axis*(Angular Velocity along X-axis^2)))+((3*Atomicity)-6)*([R]*Temperature). Here is an example- 3214.856 = ((3/2)*[R]*85)+((0.5*60*(0.610865238197901^2))+(0.5*65*(0.698131700797601^2))+(0.5*55*(0.5235987755982^2)))+((3*3)-6)*([R]*85).

How to calculate Internal Molar Energy of Non-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), Moment of Inertia along X-axis (I_x), Angular Velocity along X-axis (ω_x) & Atomicity (N) we can find Internal Molar Energy of Non-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))+(0.5*Moment of Inertia along X-axis*(Angular Velocity along X-axis^2)))+((3*Atomicity)-6)*([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)))+((3*Atomicity)-5)*([R]*Temperature)

Can the Internal Molar Energy of Non-Linear Molecule be negative?

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

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

Internal Molar Energy of Non-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 Non-Linear Molecule can be measured.

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Internal Molar Energy of Non-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 Non-Linear Molecule Example

Internal Molar Energy of Non-Linear Molecule Solution

Internal Molar Energy of Non-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 Non-Linear Molecule?

FAQs on Internal Molar Energy of Non-Linear Molecule

Variable Name

GoInternal Molar Energy of Linear Molecule given Atomicity Formula

GoInternal Molar Energy of Non-Linear Molecule given Atomicity Formula