absolute zero

Examples of absolute zero in the following topics:

• Absolute Zero

  • Absolute zero is the coldest possible temperature; formally, it is the temperature at which entropy reaches its minimum value.
  • Absolute zero is universal in the sense that all matteris in ground state at this temperature .
  • To be precise, a system at absolute zero still possesses quantum mechanical zero-point energy, the energy of its ground state.
  • The zero point of a thermodynamic temperature scale, such as the Kelvin scale, is set at absolute zero.
  • Explain why absolute zero is a natural choice as the null point for a temperature unit system

• 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 Third Law

  • According to the third law of thermodynamics, the entropy of a perfect crystal at absolute zero is exactly equal to zero.
  • The third law of thermodynamics is sometimes stated as follows: The entropy of a perfect crystal at absolute zero is exactly equal to zero.
  • Nernst proposed that the entropy of a system at absolute zero would be a well-defined constant.
  • Instead of being 0, entropy at absolute zero could be a nonzero constant, due to the fact that a system may have degeneracy (having several ground states at the same energy).
  • In simple terms, the third law states that the entropy of a perfect crystal approaches zero as the absolute temperature approaches zero.

• Kelvin Scale

  • The kelvin is a unit of measurement for temperature; the null point of the Kelvin scale is absolute zero, the lowest possible temperature.
  • The Kelvin scale is an absolute, thermodynamic temperature scale using absolute zero as its null point.
  • In the classical description of thermodynamics, absolute zero is the temperature at which all thermal motion ceases.
  • The choice of absolute zero as null point for the Kelvin scale is logical.
  • Subtracting 273.16K from the temperature of the triple point of water, 0.01°C, makes absolute zero (0K) equivalent to -273.15°C and -460°F .

• Adiabatic Processes

  • It is impossible to reduce the temperature of any system to zero temperature in a finite number of finite operations.
  • In this Atom, we discuss an adiabatic cooling process that can be used to cool a gas, as well as whether absolute zero can be obtained in real systems.
  • Previously, we learned about the third law of thermodynamics, which states: the entropy of a perfect crystal at absolute zero is exactly equal to zero.
  • Assuming an entropy difference at absolute zero, T=0 could be reached in a finite number of steps.
  • Left side: Absolute zero can be reached in a finite number of steps if S(T=0,X1)≠S(T=0, X2).

• Absolute Temperature

  • Thermodynamic temperature is an "absolute" scale because it is the measure of the fundamental property underlying temperature: its null or zero point ("absolute zero") is the temperature at which the particle constituents of matter have minimal motion and cannot become any colder.
  • Therefore, it is reasonable to choose absolute zero, where all classical motion ceases, as the reference point (T=0) of our temperature system .
  • By international agreement, the unit kelvin and its scale are defined by two points: absolute zero and the triple point of Vienna Standard Mean Ocean Water (water with a specified blend of hydrogen and oxygen isotopes).
  • Absolute zero, the lowest possible temperature, is defined precisely as 0 K and −273.15 °C.
  • Note that all of the graphs extrapolate to zero pressure at the same temperature

• Absolute Value

  • Absolute value can be thought of as the distance of a real number from zero.
  • It refers to the distance of $a$ from zero.
  • For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5, because both numbers are the same distance from 0.
  • Other names for absolute value include "numerical value," "modulus," and "magnitude."
  • The absolute values of 5 and -5 shown on a number line.

• Equations with Absolute Value

  • To solve an equation with an absolute value, first isolate the absolute value, and then solve for the positive and negative cases.
  • The absolute value of $-5$ is $5$, and the absolute value of $5$ is also $5$.  
  • Step 1: Algebraically isolate the absolute value.  
  • The absolute value term is $(2x+1)$, and it can either be 4, or –4.  
  • The absolute value of a real number may be thought of as its distance from zero.

• Matrix and Vector Norms

  • For scalars, the obvious answer is the absolute value.
  • The absolute value of a scalar has the property that it is never negative and it is zero if and only if the scalar itself is zero.

• Inequalities with Absolute Value

  • Inequalities with absolute values can be solved by considering the absolute value as the distance from 0 on the number line.
  • In this case, $\abs{x} < 10$ means "the distance between $x$ and 0 is less than 10" - in other words, you are within 10 units of zero in either direction.
  • More complicated absolute value problems should be approached using the same steps as solving equations with absolute values: algebraically isolate the absolute value and then algebraically solve for $x$.
  • First, algebraically isolate the absolute value.
  • Absolute values are always positive, so the absolute value of anything is greater than –3!