Vibrational Energy Modeled as Harmonic Oscillator Calculator

⤿

✖Momentum of Harmonic Oscillator is associated with the linear momentum.ⓘ Momentum of Harmonic Oscillator [p]			+10% -10%
✖Mass is the quantity of matter in a body regardless of its volume or of any forces acting on it.ⓘ Mass [Mass_{flight path}]			+10% -10%
✖Spring Constant is the displacement of the spring from its equilibrium position.ⓘ Spring Constant [K_spring]			+10% -10%
✖The Change in Position is known as displacement. The word displacement implies that an object has moved, or has been displaced.ⓘ Change in Position [Δx]			+10% -10%

✖Vibrational Energy is the total energy of the respective rotation-vibration levels of a diatomic molecule.ⓘ Vibrational Energy Modeled as Harmonic Oscillator [E_vf]

⎘ Copy

👎

Formula

✖

Vibrational Energy Modeled as Harmonic Oscillator

Formula

`"E"_{"vf"} = (("p"^2)/(2*"Mass"_{"flight path"}))+(0.5*"K"_{"spring"}*("Δx"^2))`

Example

`"5738.91J"=((("10kg*m/s")^2)/(2*"35.45kg"))+(0.5*"51N/m"*(("15m")^2))`

Calculator

LaTeX

Reset

👍

Download Kinetic Theory of Gases Formula PDF PDF Image

Vibrational Energy Modeled as Harmonic Oscillator Solution

STEP 0: Pre-Calculation Summary

Formula Used

Vibrational Energy = ((Momentum of Harmonic Oscillator^2)/(2*Mass))+(0.5*Spring Constant*(Change in Position^2))
E_vf = ((p^2)/(2*Mass_{flight path}))+(0.5*K_spring*(Δx^2))
This formula uses 5 Variables

Variables Used

Vibrational Energy - (Measured in Joule) - Vibrational Energy is the total energy of the respective rotation-vibration levels of a diatomic molecule.
Momentum of Harmonic Oscillator - (Measured in Kilogram Meter per Second) - Momentum of Harmonic Oscillator is associated with the linear momentum.
Mass - (Measured in Kilogram) - Mass is the quantity of matter in a body regardless of its volume or of any forces acting on it.
Spring Constant - (Measured in Newton per Meter) - Spring Constant is the displacement of the spring from its equilibrium position.
Change in Position - (Measured in Meter) - The Change in Position is known as displacement. The word displacement implies that an object has moved, or has been displaced.

STEP 1: Convert Input(s) to Base Unit

Momentum of Harmonic Oscillator: 10 Kilogram Meter per Second --> 10 Kilogram Meter per Second No Conversion Required
Mass: 35.45 Kilogram --> 35.45 Kilogram No Conversion Required
Spring Constant: 51 Newton per Meter --> 51 Newton per Meter No Conversion Required
Change in Position: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_vf = ((p^2)/(2*Mass_{flight path}))+(0.5*K_spring*(Δx^2)) --> ((10^2)/(2*35.45))+(0.5*51*(15^2))

Evaluating ... ...

E_vf = 5738.91043723554

STEP 3: Convert Result to Output's Unit

5738.91043723554 Joule --> No Conversion Required

FINAL ANSWER

5738.91043723554 ≈ 5738.91 Joule <-- Vibrational Energy

(Calculation completed in 00.020 seconds)

You are here -

Home » Chemistry » Kinetic Theory of Gases » Equipartition Principle and Heat Capacity » Vibrational Energy Modeled as Harmonic Oscillator

Credits

Created by Prerana Bakli

University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

Prerana Bakli has created this Calculator and 800+ more calculators!

Verified by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

Akshada Kulkarni has verified this Calculator and 900+ more calculators!

< 24 Equipartition Principle and Heat Capacity Calculators

Internal Molar Energy of Non-Linear Molecule

Go 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)

Average Thermal Energy of Non-linear Polyatomic Gas Molecule

Go Thermal Energy = ((3/2)*[BoltZ]*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)-6)*([BoltZ]*Temperature)

Average Thermal Energy of Linear Polyatomic Gas Molecule

Internal Molar Energy of Linear Molecule

Rotational Energy of Non-Linear Molecule

Go Rotational Energy = (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)

Translational Energy

Go Translational Energy = ((Momentum along X-axis^2)/(2*Mass))+((Momentum along Y-axis^2)/(2*Mass))+((Momentum along Z-axis^2)/(2*Mass))

Rotational Energy of Linear Molecule

Go Rotational Energy = (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))

Vibrational Energy Modeled as Harmonic Oscillator

Go Vibrational Energy = ((Momentum of Harmonic Oscillator^2)/(2*Mass))+(0.5*Spring Constant*(Change in Position^2))

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

Go Thermal Energy given Atomicity = ((6*Atomicity)-6)*(0.5*[BoltZ]*Temperature)

Average Thermal Energy of Linear Polyatomic Gas Molecule given Atomicity

Go Thermal Energy given Atomicity = ((6*Atomicity)-5)*(0.5*[BoltZ]*Temperature)

Total Kinetic Energy

Go Total Energy = Translational Energy+Rotational Energy+Vibrational Energy

Specific Heat Capacity given heat capacity

Go Specific Heat Capacity = Heat Capacity/(Mass*Change in Temperature)

Internal Molar Energy of Non-Linear Molecule given Atomicity

Go Molar Internal Energy = ((6*Atomicity)-6)*(0.5*[R]*Temperature)

Internal Molar Energy of Linear Molecule given Atomicity

Go Molar Internal Energy = ((6*Atomicity)-5)*(0.5*[R]*Temperature)

Heat Capacity

Go Heat Capacity = Mass*Specific Heat Capacity*Change in Temperature

Molar Vibrational Energy of Non-Linear Molecule

Go Vibrational Molar Energy = ((3*Atomicity)-6)*([R]*Temperature)

Molar Vibrational Energy of Linear Molecule

Go Vibrational Molar Energy = ((3*Atomicity)-5)*([R]*Temperature)

Vibrational Energy of Non-Linear Molecule

Go Vibrational Energy = ((3*Atomicity)-6)*([BoltZ]*Temperature)

Vibrational Energy of Linear Molecule

Go Vibrational Energy = ((3*Atomicity)-5)*([BoltZ]*Temperature)

Heat Capacity given Specific Heat Capacity

Go Heat Capacity = Specific Heat Capacity*Mass

Number of Modes in Non-Linear Molecule

Go Number of Normal modes for Non Linear = (6*Atomicity)-6

Vibrational Mode of Non-Linear Molecule

Go Number of Normal modes = (3*Atomicity)-6

Vibrational Mode of Linear Molecule

Go Number of Normal modes = (3*Atomicity)-5

Number of Modes in Linear Molecule

Go Number of Modes = (6*Atomicity)-5

Vibrational Energy Modeled as Harmonic Oscillator Formula

Vibrational Energy = ((Momentum of Harmonic Oscillator^2)/(2*Mass))+(0.5*Spring Constant*(Change in Position^2))
E_vf = ((p^2)/(2*Mass_{flight path}))+(0.5*K_spring*(Δx^2))

What is the statement of Equipartition Theorem?

The original concept of equipartition was that the total kinetic energy of a system is shared equally among all of its independent parts, on the average, once the system has reached thermal equilibrium. Equipartition also makes quantitative predictions for these energies. The key point is that the kinetic energy is quadratic in the velocity. The equipartition theorem shows that in thermal equilibrium, any degree of freedom (such as a component of the position or velocity of a particle) which appears only quadratically in the energy has an average energy of 1⁄2kBT and therefore contributes 1⁄2kB to the system's heat capacity.

How to Calculate Vibrational Energy Modeled as Harmonic Oscillator?

Vibrational Energy Modeled as Harmonic Oscillator calculator uses Vibrational Energy = ((Momentum of Harmonic Oscillator^2)/(2*Mass))+(0.5*Spring Constant*(Change in Position^2)) to calculate the Vibrational Energy, The Vibrational energy modeled as harmonic oscillator is the kinetic energy an object has due to its vibrational motion. Vibrational Energy is denoted by E_vf symbol.

How to calculate Vibrational Energy Modeled as Harmonic Oscillator using this online calculator? To use this online calculator for Vibrational Energy Modeled as Harmonic Oscillator, enter Momentum of Harmonic Oscillator (p), Mass (Mass_{flight path}), Spring Constant (K_spring) & Change in Position (Δx) and hit the calculate button. Here is how the Vibrational Energy Modeled as Harmonic Oscillator calculation can be explained with given input values -> 5738.91 = ((10^2)/(2*35.45))+(0.5*51*(15^2)).

FAQ

What is Vibrational Energy Modeled as Harmonic Oscillator?

The Vibrational energy modeled as harmonic oscillator is the kinetic energy an object has due to its vibrational motion and is represented as E_vf = ((p^2)/(2*Mass_{flight path}))+(0.5*K_spring*(Δx^2)) or Vibrational Energy = ((Momentum of Harmonic Oscillator^2)/(2*Mass))+(0.5*Spring Constant*(Change in Position^2)). Momentum of Harmonic Oscillator is associated with the linear momentum, Mass is the quantity of matter in a body regardless of its volume or of any forces acting on it, Spring Constant is the displacement of the spring from its equilibrium position & The Change in Position is known as displacement. The word displacement implies that an object has moved, or has been displaced.

How to calculate Vibrational Energy Modeled as Harmonic Oscillator?

The Vibrational energy modeled as harmonic oscillator is the kinetic energy an object has due to its vibrational motion is calculated using Vibrational Energy = ((Momentum of Harmonic Oscillator^2)/(2*Mass))+(0.5*Spring Constant*(Change in Position^2)). To calculate Vibrational Energy Modeled as Harmonic Oscillator, you need Momentum of Harmonic Oscillator (p), Mass (Mass_{flight path}), Spring Constant (K_spring) & Change in Position (Δx). With our tool, you need to enter the respective value for Momentum of Harmonic Oscillator, Mass, Spring Constant & Change in Position and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Vibrational Energy?

In this formula, Vibrational Energy uses Momentum of Harmonic Oscillator, Mass, Spring Constant & Change in Position. We can use 2 other way(s) to calculate the same, which is/are as follows -

Vibrational Energy = ((3*Atomicity)-5)*([BoltZ]*Temperature)
Vibrational Energy = ((3*Atomicity)-6)*([BoltZ]*Temperature)

Home

FREE PDFs

🔍 Search