absolute zero

Examples of absolute zero in the following topics:

• The Third Law of Thermodynamics and Absolute Energy

  • The entropy of a system at absolute zero is typically zero, and in all cases is determined only by the number of different ground states it has.
  • Specifically, the entropy of a pure crystalline substance at absolute zero temperature is zero.
  • At absolute zero there is only 1 microstate possible (Ω=1) and ln(1) = 0.
  • The entropy determined relative to this point (absolute zero) is the absolute entropy.
  • For the entropy at absolute zero to be zero, the magnetic moments of a perfectly ordered crystal must themselves be perfectly ordered.

• The Three Laws of Thermodynamics

  • The third law of thermodynamics states that the entropy of a system approaches a constant value as the temperature approaches absolute zero.
  • The entropy of a system at absolute zero is typically zero, and in all cases is determined only by the number of different ground states it has.
  • Specifically, the entropy of a pure crystalline substance (perfect order) at absolute zero temperature is zero.

• Charles' and Gay-Lussac's Law: Temperature and Volume

  • If a gas contracts by 1/273 of its volume for each degree of cooling, it should contract to zero volume at a temperature of –273°C; this is the lowest possible temperature in the universe, known as absolute zero.
  • The lower a gas' pressure, the greater its volume (Boyle's Law), so at low pressures, the fraction \frac{V}{273} will have a larger value; therefore, the gas must "contract faster" to reach zero volume when its starting volume is larger.

• Kinetic Molecular Theory and Gas Laws

  • The average kinetic energy of gas molecules is directly proportional to absolute temperature only; this implies that all molecular motion ceases if the temperature is reduced to absolute zero.
  • Boyle's Law states that at constant temperature, the absolute pressure and volume of a given mass of confined gas are inversely proportional.

• Bond Enthalpy

  • Thus, the change in enthalpy, $\Delta H$, is a more useful quantity than its absolute value.
  • Bond enthalpy, also known as bond dissociation energy, is defined as the standard enthalpy change when a bond is cleaved by homolysis, with reactants and products of the homolysis reaction at 0 K (absolute zero).

• Distribution of Molecular Speeds and Collision Frequency

  • According to the Kinetic Molecular Theory, all gaseous particles are in constant random motion at temperatures above absolute zero.
  • Measuring the velocities of particles at a given time results in a large distribution of values; some particles may move very slowly, others very quickly, and because they are constantly moving in different directions, the velocity could equal zero.
  • In the above formula, R is the gas constant, T is absolute temperature, and Mm is the molar mass of the gas particles in kg/mol.

• Temperature

  • The ability to measure temperature accurately was a major scientific advancement, putting absolute numbers on an observable phenomenon.
  • How cold is absolute 0?"
  • Therefore, the temperature must be "absolute 0."
  • The question remains: how much colder is absolute 0 than 0 °C?
  • In 1848, Lord Kelvin (William Thomson) wrote a paper entitled "On An Absolute Thermometric Scale" about the need to seek out a thermodynamic zero temperature.

• Van der Waals Equation

  • Derived by Johannes Diderik van der Waals in 1873, the van der Waals equation modifies the Ideal Gas Law; it predicts the properties of real gases by describing particles of non-zero volume governed by pairwise attractive forces.
  • where P is the pressure, V is the volume, R is the universal gas constant, and T is the absolute temperature.
  • Notice that the van der Waals equation becomes the Ideal Gas Law as these two correction terms approach zero.

• The Arrhenius Equation

  • In this equation, k is the rate constant, T is the absolute temperature, Ea is the activation energy, A is the pre-exponential factor, and R is the universal gas constant.
  • Depending on the magnitudes of Ea and the temperature, this fraction can range from zero, where no molecules have enough energy to react, to unity, where all molecules have enough energy to react.
  • This could only occur if either the activation energy were zero, or if the kinetic energy of all molecules exceeded Ea—both of which are highly unlikely scenarios.
  • While "barrier-less" reactions, which have zero activation energy, have been observed, these are rare, and even in such cases, molecules will most likely need to collide with the right orientation in order to react.

• Particle in a Box

  • A may be any complex number with absolute value $\left| A \right| =\sqrt { \frac { 2 }{ L } }$
  • Note that just like a guitar string, the solutions to the particle in a box problem are constrained to those wavefunctions that anchor the amplitude at the walls of the box as zero.
  • Inside the box the potential V(x) is zero.