## 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)
Umolar = ((3/2)*[R]*T)+((0.5*Iy*(ωy^2))+(0.5*Iz*(ωz^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
Umolar = ((3/2)*[R]*T)+((0.5*Iy*(ωy^2))+(0.5*Iz*(ωz^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 ... ...
Umolar = 3914.0460699927
STEP 3: Convert Result to Output's Unit
3914.0460699927 Joule --> No Conversion Required
3914.0460699927 3914.046 Joule <-- Molar Internal Energy
(Calculation completed in 00.004 seconds)
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## Credits

Created by Prerana Bakli
University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA
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## <Equipartition Principle and Heat Capacity Calculators

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))

## <Important Formulae on Equipartition Principle and Heat Capacity Calculators

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)
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)

## Internal Molar Energy of Linear Molecule 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)))+((3*Atomicity)-5)*([R]*Temperature)
Umolar = ((3/2)*[R]*T)+((0.5*Iy*(ωy^2))+(0.5*Iz*(ωz^2)))+((3*N)-5)*([R]*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 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 Umolar 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 (Iy), Angular Velocity along Y-axis y), Moment of Inertia along Z-axis (Iz), Angular Velocity along Z-axis 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 Umolar = ((3/2)*[R]*T)+((0.5*Iy*(ωy^2))+(0.5*Iz*(ωz^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 (Iy), Angular Velocity along Y-axis y), Moment of Inertia along Z-axis (Iz), Angular Velocity along Z-axis 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 3 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)
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