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

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✖The Atomicity is defined as the total number of atoms present in a molecule or element.ⓘ Atomicity [N]			+10% -10%
✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature [T]			+10% -10%

✖Thermal Energy given Atomicity is the input heat energy to a given system. This input heat energy is converted into useful work and a part of it is wasted in doing so.ⓘ Average Thermal Energy of Non-linear polyatomic Gas Molecule given Atomicity [Q_atomicity]

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Formula

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

Formula

`"Q"_{"atomicity"} = ((6*"N")-6)*(0.5*"[BoltZ]"*"T")`

Example

`"7E^-21J"=((6*"3")-6)*(0.5*"[BoltZ]"*"85K")`

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

STEP 0: Pre-Calculation Summary

Formula Used

Thermal Energy given Atomicity = ((6*Atomicity)-6)*(0.5*[BoltZ]*Temperature)
Q_atomicity = ((6*N)-6)*(0.5*[BoltZ]*T)
This formula uses 1 Constants, 3 Variables

Constants Used

[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23

Variables Used

Thermal Energy given Atomicity - (Measured in Joule) - Thermal Energy given Atomicity is the input heat energy to a given system. This input heat energy is converted into useful work and a part of it is wasted in doing so.
Atomicity - The Atomicity is defined as the total number of atoms present in a molecule or element.
Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.

STEP 1: Convert Input(s) to Base Unit

Atomicity: 3 --> No Conversion Required
Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q_atomicity = ((6*N)-6)*(0.5*[BoltZ]*T) --> ((6*3)-6)*(0.5*[BoltZ]*85)

Evaluating ... ...

Q_atomicity = 7.041307452E-21

STEP 3: Convert Result to Output's Unit

7.041307452E-21 Joule --> No Conversion Required

FINAL ANSWER

7.041307452E-21 ≈ 7E-21 Joule <-- Thermal Energy given Atomicity

(Calculation completed in 00.004 seconds)

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Home » Chemistry » Kinetic Theory of Gases » Equipartition Principle and Heat Capacity » Average Thermal Energy of Non-linear polyatomic Gas Molecule given Atomicity

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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

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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

< 20 Important Formulae on Equipartition Principle and Heat Capacity Calculators

Internal Molar Energy of Non-Linear Molecule

Internal Molar Energy of Linear Molecule

Atomicity given Molar Heat Capacity at Constant Pressure and Volume of Linear Molecule

Go Atomicity = ((2.5*( Molar Specific Heat Capacity at Constant Pressure/Molar Specific Heat Capacity at Constant Volume))-1.5)/((3*(Molar Specific Heat Capacity at Constant Pressure/Molar Specific Heat Capacity at Constant Volume))-3)

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))

Molar Heat Capacity at Constant Pressure given Compressibility

Go Molar Specific Heat Capacity at Constant Pressure = (Isothermal Compressibility/Isentropic Compressibility)*Molar Specific Heat Capacity at Constant Volume

Ratio of Molar Heat Capacity of Linear Molecule

Go Ratio of Molar Heat Capacity = ((((3*Atomicity)-2.5)*[R])+[R])/(((3*Atomicity)-2.5)*[R])

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

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)

Atomicity given Molar Vibrational Energy of Non-Linear Molecule

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

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)

Atomicity given Ratio of Molar Heat Capacity of Linear Molecule

Go Atomicity = ((2.5*Ratio of Molar Heat Capacity)-1.5)/((3*Ratio of Molar Heat Capacity)-3)

Number of Modes in Non-Linear Molecule

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

Ratio of Molar Heat Capacity given Degree of Freedom

Go Ratio of Molar Heat Capacity = 1+(2/Degree of Freedom)

Degree of Freedom given Ratio of Molar Heat Capacity

Go Degree of Freedom = 2/(Ratio of Molar Heat Capacity-1)

Vibrational Mode of Linear Molecule

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

Atomicity given Vibrational Degree of Freedom in Non-Linear Molecule

Go Atomicity = (Degree of Freedom+6)/3

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

Thermal Energy given Atomicity = ((6*Atomicity)-6)*(0.5*[BoltZ]*Temperature)
Q_atomicity = ((6*N)-6)*(0.5*[BoltZ]*T)

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

Average Thermal Energy of Non-linear polyatomic Gas Molecule given Atomicity calculator uses Thermal Energy given Atomicity = ((6*Atomicity)-6)*(0.5*[BoltZ]*Temperature) to calculate the Thermal Energy given Atomicity, The Average thermal energy of non-linear polyatomic gas molecule given atomicity is produced when a rise in temperature causes atoms and molecules to move faster and collide with each other. Thermal Energy given Atomicity is denoted by Q_atomicity symbol.

How to calculate Average Thermal Energy of Non-linear polyatomic Gas Molecule given Atomicity using this online calculator? To use this online calculator for Average Thermal Energy of Non-linear polyatomic Gas Molecule given Atomicity, enter Atomicity (N) & Temperature (T) and hit the calculate button. Here is how the Average Thermal Energy of Non-linear polyatomic Gas Molecule given Atomicity calculation can be explained with given input values -> 7E-21 = ((6*3)-6)*(0.5*[BoltZ]*85).

FAQ

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

The Average thermal energy of non-linear polyatomic gas molecule given atomicity is produced when a rise in temperature causes atoms and molecules to move faster and collide with each other and is represented as Q_atomicity = ((6*N)-6)*(0.5*[BoltZ]*T) or Thermal Energy given Atomicity = ((6*Atomicity)-6)*(0.5*[BoltZ]*Temperature). The Atomicity is defined as the total number of atoms present in a molecule or element & Temperature is the degree or intensity of heat present in a substance or object.

How to calculate Average Thermal Energy of Non-linear polyatomic Gas Molecule given Atomicity?

The Average thermal energy of non-linear polyatomic gas molecule given atomicity is produced when a rise in temperature causes atoms and molecules to move faster and collide with each other is calculated using Thermal Energy given Atomicity = ((6*Atomicity)-6)*(0.5*[BoltZ]*Temperature). To calculate Average Thermal Energy of Non-linear polyatomic Gas Molecule given Atomicity, you need Atomicity (N) & Temperature (T). With our tool, you need to enter the respective value for Atomicity & Temperature 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 Thermal Energy given Atomicity?

In this formula, Thermal Energy given Atomicity uses Atomicity & Temperature. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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