Internal Molar Energy of Linear Molecule Calculator

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✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature [T]			+10% -10%
✖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.ⓘ Moment of Inertia along Y-axis [I_y]			+10% -10%
✖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.ⓘ Angular Velocity along Y-axis [ω_y]			+10% -10%
✖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.ⓘ Moment of Inertia along Z-axis [I_z]			+10% -10%
✖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.ⓘ Angular Velocity along Z-axis [ω_z]			+10% -10%
✖The Atomicity is defined as the total number of atoms present in a molecule or element.ⓘ Atomicity [N]			+10% -10%

✖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.ⓘ Internal Molar Energy of Linear Molecule [U_molar]

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Formula

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Internal Molar Energy of Linear Molecule

Formula

`"U"_{"molar"} = ((3/2)*"[R]"*"T")+((0.5*"I"_{"y"}*("ω"_{"y"}^2))+(0.5*"I"_{"z"}*("ω"_{"z"}^2)))+((3*"N")-5)*("[R]"*"T")`

Example

`"3914.046J"=((3/2)*"[R]"*"85K")+((0.5*"60kg·m²"*(("35degree/s")^2))+(0.5*"65kg·m²"*(("40degree/s")^2)))+((3*"3")-5)*("[R]"*"85K")`

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Internal Molar Energy of Linear Molecule Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
U_molar = ((3/2)*[R]*T)+((0.5*I_y*(ω_y^2))+(0.5*I_z*(ω_z^2)))+((3*N)-5)*([R]*T)
This formula uses 1 Constants, 7 Variables

Constants Used

[R] - Universal gas constant Value Taken As 8.31446261815324

Variables Used

Molar Internal Energy - (Measured in Joule) - 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.
Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.
Moment of Inertia along Y-axis - (Measured in Kilogram Square Meter) - 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.
Angular Velocity along Y-axis - (Measured in Radian per Second) - 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.
Moment of Inertia along Z-axis - (Measured in Kilogram Square Meter) - 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.
Angular Velocity along Z-axis - (Measured in Radian per Second) - 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.
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

Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required
Moment of Inertia along Y-axis: 60 Kilogram Square Meter --> 60 Kilogram Square Meter No Conversion Required
Angular Velocity along Y-axis: 35 Degree per Second --> 0.610865238197901 Radian per Second (Check conversion here)
Moment of Inertia along Z-axis: 65 Kilogram Square Meter --> 65 Kilogram Square Meter No Conversion Required
Angular Velocity along Z-axis: 40 Degree per Second --> 0.698131700797601 Radian per Second (Check conversion here)
Atomicity: 3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

U_molar = ((3/2)*[R]*T)+((0.5*I_y*(ω_y^2))+(0.5*I_z*(ω_z^2)))+((3*N)-5)*([R]*T) --> ((3/2)*[R]*85)+((0.5*60*(0.610865238197901^2))+(0.5*65*(0.698131700797601^2)))+((3*3)-5)*([R]*85)

Evaluating ... ...

U_molar = 3914.0460699927

STEP 3: Convert Result to Output's Unit

3914.0460699927 Joule --> No Conversion Required

FINAL ANSWER

3914.0460699927 ≈ 3914.046 Joule <-- Molar Internal Energy

(Calculation completed in 00.004 seconds)

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Home » Chemistry » Kinetic Theory of Gases » Equipartition Principle and Heat Capacity » Internal Molar Energy of Linear Molecule

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Created by Prerana Bakli

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

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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

Internal Molar Energy of Linear Molecule Formula

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 Internal Molar Energy of Linear Molecule?

Internal Molar Energy of Linear Molecule calculator 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 calculate 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 calculate Internal Molar Energy of Linear Molecule using this online calculator? To use this online calculator 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. Here is how the Internal Molar Energy of Linear Molecule calculation can be explained with given input values -> 3914.046 = ((3/2)*[R]*85)+((0.5*60*(0.610865238197901^2))+(0.5*65*(0.698131700797601^2)))+((3*3)-5)*([R]*85).

FAQ

What is Internal Molar Energy of Linear Molecule?

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 and is represented as U_molar = ((3/2)*[R]*T)+((0.5*I_y*(ω_y^2))+(0.5*I_z*(ω_z^2)))+((3*N)-5)*([R]*T) or 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). Temperature is the degree or intensity of heat present in a substance or object, 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, 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, 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, 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 & The Atomicity is defined as the total number of atoms present in a molecule or element.

How to calculate Internal Molar Energy of Linear Molecule?

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 is calculated using 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 calculate Internal Molar Energy of Linear Molecule, you need 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). With our tool, you need to enter the respective value for Temperature, Moment of Inertia along Y-axis, Angular Velocity along Y-axis, Moment of Inertia along Z-axis, Angular Velocity along Z-axis & Atomicity 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 Molar Internal Energy?

In this formula, Molar Internal Energy uses Temperature, Moment of Inertia along Y-axis, Angular Velocity along Y-axis, Moment of Inertia along Z-axis, Angular Velocity along Z-axis & Atomicity. We can use 6 other way(s) to calculate the same, which is/are as follows -

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

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