Number of Modes in Linear Molecule Calculator

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Ratio of Molar Heat Capacity

Atomicity

Degree of Freedom

Molar Heat Capacity

Temperature

✖The Atomicity is defined as the total number of atoms present in a molecule or element.ⓘ Atomicity [N]

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✖The Number of Modes is the fundamental modes responsible for various factors of kinetic energy.ⓘ Number of Modes in Linear Molecule [M_n]

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Formula

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Number of Modes in Linear Molecule

Formula

`"M"_{"n"} = (6*"N")-5`

Example

`"13"=(6*"3")-5`

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Number of Modes in Linear Molecule Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Modes = (6*Atomicity)-5
M_n = (6*N)-5
This formula uses 2 Variables

Variables Used

Number of Modes - The Number of Modes is the fundamental modes responsible for various factors of kinetic energy.
Atomicity - The Atomicity is defined as the total number of atoms present in a molecule or element.

STEP 1: Convert Input(s) to Base Unit

Atomicity: 3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_n = (6*N)-5 --> (6*3)-5

Evaluating ... ...

M_n = 13

STEP 3: Convert Result to Output's Unit

13 --> No Conversion Required

FINAL ANSWER

13 <-- Number of Modes

(Calculation completed in 00.004 seconds)

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Home » Chemistry » Kinetic Theory of Gases » Equipartition Principle and Heat Capacity » Number of Modes in Linear Molecule

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Created by Prerana Bakli

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

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Verified by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

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< 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

< 1 Real Gas Calculators

Number of Modes in Linear Molecule

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

Number of Modes in Linear Molecule Formula

Number of Modes = (6*Atomicity)-5
M_n = (6*N)-5

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 Number of Modes in Linear Molecule?

Number of Modes in Linear Molecule calculator uses Number of Modes = (6*Atomicity)-5 to calculate the Number of Modes, The Number of modes in Linear Molecule is the number of variables required to describe the motion of a particle completely. Number of Modes is denoted by M_n symbol.

How to calculate Number of Modes in Linear Molecule using this online calculator? To use this online calculator for Number of Modes in Linear Molecule, enter Atomicity (N) and hit the calculate button. Here is how the Number of Modes in Linear Molecule calculation can be explained with given input values -> 13 = (6*3)-5.

FAQ

What is Number of Modes in Linear Molecule?

The Number of modes in Linear Molecule is the number of variables required to describe the motion of a particle completely and is represented as M_n = (6*N)-5 or Number of Modes = (6*Atomicity)-5. The Atomicity is defined as the total number of atoms present in a molecule or element.

How to calculate Number of Modes in Linear Molecule?

The Number of modes in Linear Molecule is the number of variables required to describe the motion of a particle completely is calculated using Number of Modes = (6*Atomicity)-5. To calculate Number of Modes in Linear Molecule, you need Atomicity (N). With our tool, you need to enter the respective value for Atomicity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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