Examples of degree of freedom in the following topics:
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- In this case, the kinetic energy consists only of the translational energy of the individual atoms.
- Note that there are three degrees of freedom in monatomic gases: translation in x, y and z directions.
- Since atomic motion is random (and therefore isotropic), each degrees of freedom contribute $\frac{1}{2}kT$ per atom to the internal energy.
- A diatomic molecule (H2, O2, N2, etc.) has 5 degrees of freedom (3 for translation in x, y and z directions, and 2 for rotation).
- Determine the number of degrees of freedom and calculate the internal energy for an ideal gas molecule
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- This is much cleaner than writing out all the components and has the additional advantage that we can add more masses/springs without changing the equations, we just have to incorporate the additional terms into the definition of $M$ and $K$ .
- If $\Omega = 0$ , then the equations of motion reduce to those for two uncoupled oscillators with the same characteristic frequency $\omega_0$ .
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- The kinetic theory of gases describes a gas as a large number of small particles (atoms or molecules), all of which are in constant, random motion.
- Also, the temperature of an ideal monatomic gas is a measure of the average kinetic energy of its atoms, as illustrated in .
- The kinetic theory of gases uses the model of the ideal gas to relate temperature to the average translational kinetic energy of the molecules in a container of gas in thermodynamic equilibrium .
- In kinetic theory, the temperature of a classical ideal gas is related to its average kinetic energy per degree of freedom Ek via the equation:
- (R: ideal gas constant, n: number of moles of gas) from a microscopic theory.
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- For example, in the collision of macroscopic bodies, some kinetic energy is turned into vibrational energy of the constituent atoms.
- Another example in which kinetic energy is transformed into another form of energy is when the molecules of a gas or liquid collide.
- When this happens, kinetic energy is often exchanged between the molecules' translational motion and their internal degrees of freedom.
- Let us consider an example of a two-body sliding block system.
- where mais the mass of the incoming block, ua is the velocity of the incoming block, mbis the mass of the initially stationary block, ubis the velocity of initially stationary block (0 m/s), and v is the final velocity the two body system.
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- The heat capacity at constant volume of nR = 1 J·K−1 of any gas, including an ideal gas is:
- The heat capacity at constant pressure of 1 J·K−1 ideal gas is:
- Julius Robert von Mayer (November 25, 1814 – March 20, 1878), a German physician and physicist, was one of the founders of thermodynamics.
- He is best known for his 1841 enunciation of one of the original statements of the conservation of energy (or what is now known as one of the first versions of the first law of thermodynamics): "Energy can be neither created nor destroyed. " In 1842, Mayer described the vital chemical process now referred to as oxidation as the primary source of energy for any living creature.
- Potential energy stored in these internal degrees of freedom contributes to specific heat of the gas.
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- When we studied the Zeeman effect we saw that in the absence of a magnetic field, all three degrees of freedom oscillated with the same frequency.
- The expression we derived for the frequency of oscillation was
- What sort of pattern of nodal lines would we see?
- Therefore we have proved that if the ratio of the lengths of the sides of the drum is irrational, then there is no degeneracy.
- Figure 2.5: The sum of the two modes 12 and 21.
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- In the Fahrenheit scale, the freezing of water is defined at 32 degrees, while the boiling point of water is defined to be 212 degrees.
- The unit of this scale is the degree Fahrenheit (°F).
- The second determining point, 32 degrees, was a mixture of just ice and water at a 1:1 ratio.
- On the Celsius scale, the freezing and boiling points of water are 100 degrees apart.
- A temperature interval of 1 °F is equal to an interval of 5/9 degrees Celsius (°C).
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- The Kelvin scale is named after Glasgow University engineer and physicist William Thomson, 1st Baron Kelvin (1824-1907), who wrote of the need for an "absolute thermometric scale. " Unlike the degree Fahrenheit and the degree Celsius, the kelvin is not referred to or typeset as a degree.
- The kelvin is the primary unit of measurement in the physical sciences, but it is often used in conjunction with the degree Celsius, which has the same magnitude.
- The kelvin is defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water (exactly 0.01°C, or 32.018°F).
- To convert kelvin to degrees Celsius, we use the following formula:
- Relationships between the Fahrenheit, Celsius, and Kelvin temperature scales, rounded to the nearest degree.
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- The unit of measurement is the degree Celsius (°C).
- The temperature of the triple point of water is defined as precisely 273.16K and 0.01°C.
- Based on this, the relationship between degree Celsius and Kelvin is as follows:
- Besides expressing specific temperatures along its scale (e.g., "Gallium melts at 29.7646°C" and "The temperature outside is 23 degrees Celsius"), the degree Celsius is also suitable for expressing temperature intervals -- differences between temperatures, or their uncertainties (e.g.
- "The output of the heat exchanger is hotter by 40 degrees Celsius" and "Our standard uncertainty is ±3°C").
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- The box is being pushed at an angle of 45 degrees to the x direction?
- The box is being pushed at an angle of 60 degrees to the x direction?
- The box is being pushed at an angle of 90 degrees to the x direction?
- In the second scenario, the box is being pushed at an angle of 45 degrees to the x-direction; and thus also a 45 degree angle to the y-direction.
- When evaluated, cosine of 60 degrees is equal to 1/2.