Degree of Freedom given Ratio of Molar Heat Capacity Solution

STEP 0: Pre-Calculation Summary
Formula Used
Degree of Freedom = 2/(Ratio of Molar Heat Capacity-1)
F = 2/(γ-1)
This formula uses 2 Variables
Variables Used
Degree of Freedom - Degree of Freedom is an independent physical parameter in the formal description of the state of a physical system.
Ratio of Molar Heat Capacity - The Ratio of Molar Heat Capacity is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume.
STEP 1: Convert Input(s) to Base Unit
Ratio of Molar Heat Capacity: 1.5 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
F = 2/(γ-1) --> 2/(1.5-1)
Evaluating ... ...
F = 4
STEP 3: Convert Result to Output's Unit
4 --> No Conversion Required
FINAL ANSWER
4 <-- Degree of Freedom
(Calculation completed in 00.004 seconds)

Credits

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University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA
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6 Degree of Freedom Calculators

Degree of Freedom given Molar Heat Capacity at Constant Pressure
Go Degree of Freedom = 2/((Molar Specific Heat Capacity at Constant Pressure/(Molar Specific Heat Capacity at Constant Pressure-[R]))-1)
Degree of Freedom given Molar Heat Capacity at Constant Volume
Go Degree of Freedom = 2/(((Molar Specific Heat Capacity at Constant Volume+[R])/Molar Specific Heat Capacity at Constant Volume)-1)
Degree of Freedom given Molar Heat Capacity at Constant Volume and Pressure
Go Degree of Freedom = 2/((Molar Specific Heat Capacity at Constant Pressure/Molar Specific Heat Capacity at Constant Volume)-1)
Degree of Freedom given Ratio of Molar Heat Capacity
Go Degree of Freedom = 2/(Ratio of Molar Heat Capacity-1)
Degree of Freedom in Non-Linear Molecule
Go Degree of Freedom = (6*Atomicity)-6
Degree of Freedom in Linear Molecule
Go Degree of Freedom = (6*Atomicity)-5

20 Important Formulae on 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)
Internal Molar Energy of 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)))+((3*Atomicity)-5)*([R]*Temperature)
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

Degree of Freedom given Ratio of Molar Heat Capacity Formula

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

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 Degree of Freedom given Ratio of Molar Heat Capacity?

Degree of Freedom given Ratio of Molar Heat Capacity calculator uses Degree of Freedom = 2/(Ratio of Molar Heat Capacity-1) to calculate the Degree of Freedom, The Degree of Freedom given Ratio of Molar Heat Capacity is the number of variables required to describe the motion of a particle completely. Degree of Freedom is denoted by F symbol.

How to calculate Degree of Freedom given Ratio of Molar Heat Capacity using this online calculator? To use this online calculator for Degree of Freedom given Ratio of Molar Heat Capacity, enter Ratio of Molar Heat Capacity (γ) and hit the calculate button. Here is how the Degree of Freedom given Ratio of Molar Heat Capacity calculation can be explained with given input values -> 4 = 2/(1.5-1).

FAQ

What is Degree of Freedom given Ratio of Molar Heat Capacity?
The Degree of Freedom given Ratio of Molar Heat Capacity is the number of variables required to describe the motion of a particle completely and is represented as F = 2/(γ-1) or Degree of Freedom = 2/(Ratio of Molar Heat Capacity-1). The Ratio of Molar Heat Capacity is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume.
How to calculate Degree of Freedom given Ratio of Molar Heat Capacity?
The Degree of Freedom given Ratio of Molar Heat Capacity is the number of variables required to describe the motion of a particle completely is calculated using Degree of Freedom = 2/(Ratio of Molar Heat Capacity-1). To calculate Degree of Freedom given Ratio of Molar Heat Capacity, you need Ratio of Molar Heat Capacity (γ). With our tool, you need to enter the respective value for Ratio of Molar Heat Capacity 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 Degree of Freedom?
In this formula, Degree of Freedom uses Ratio of Molar Heat Capacity. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • Degree of Freedom = (6*Atomicity)-5
  • Degree of Freedom = (6*Atomicity)-6
  • Degree of Freedom = 2/((Molar Specific Heat Capacity at Constant Pressure/(Molar Specific Heat Capacity at Constant Pressure-[R]))-1)
  • Degree of Freedom = 2/((Molar Specific Heat Capacity at Constant Pressure/Molar Specific Heat Capacity at Constant Volume)-1)
  • Degree of Freedom = 2/(((Molar Specific Heat Capacity at Constant Volume+[R])/Molar Specific Heat Capacity at Constant Volume)-1)
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