Triple point

Examples of Triple point in the following topics:

• Solid to Gas Phase Transition

  • But at temperatures below that of the triple point, a decrease in pressure will result in a phase transition directly from the solid to the gaseous.
  • Also, at pressures below the triple point pressure, an increase in temperature will result in a solid being converted to gas without passing through the liquid region.
  • This is because the pressure of their triple point is very high and it is difficult to obtain them as liquids.
  • Notice the triple point of the substance.
  • At temperatures and pressures below those of the triple point, a phase change between the solid and gas phases can take place.

• Major Features of a Phase Diagram

  • The major features of a phase diagram are phase boundaries and the triple point.
  • The triple point is the point on the phase diagram where the lines of equilibrium intersect -- the point at which all three distinct phases of matter (solid, liquid, gas) coexist.
  • At the triple point, water in the solid, liquid, and gaseous states coexist.
  • The green line marks the freezing point (or transition from liquid to solid), the blue line marks the boiling point (or transition from liquid to gas), and the red line shows the conditions under which a solid can be converted directly to a gas (and vice-versa).

• 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.
  • The choice of absolute zero as null point for the Kelvin scale is logical.
  • 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).
  • 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 .

• 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).
  • The triple point of water is defined precisely as 273.16 K and 0.01 °C.

• Freezing Point Depression

  • Freezing point depression is the phenomena that describes why adding a solute to a solvent results in the lowering of the freezing point of the solvent.
  • In this equation, $\Delta T_f$ is the freezing point depression, Kf is the freezing point depression constant, and i is the van 't Hoff factor.
  • The value of 0.93 oC is the change in the freezing point.
  • A triple phase diagram which shows the pressure and temperature of the normal boiling and freezing points of a solvent (green lines) and the boiling and freezing points of a solution (purple lines).
  • Discuss the effects of a solute on the freezing point of a solvent

• Double and Triple Covalent Bonds

  • Hybridization describes the bonding situation from a specific atom's point of view.
  • The simplest triple-bonded organic compound is acetylene, C2H2.
  • Similar to double bonds, no rotation around the triple bond axis is possible.
  • In this case, four orbitals are produced which point along the direction of the vertices of a tetrahedron.
  • Describe the types of orbital overlap that occur in single, double, and triple bonds

• Center of Mass and Inertia

  • The center of mass for a rigid body can be expressed as a triple integral.
  • The center of mass is the unique point at the center of a distribution of mass in space that has the property that the weighted position vectors relative to this point sum to zero.
  • If the mass distribution is continuous with the density $\rho (r)$ within a volume $V$, then the integral of the weighted position coordinates of the points in this volume relative to the center of mass $\mathbf{R}$ is zero; that is:
  • The integral is over the three dimensional volume, so it is a triple integral.

• Applications of Multiple Integrals

  • In mechanics, the moment of inertia is calculated as the volume integral (triple integral) of the density weighed with the square of the distance from the axis:
  • In the following example, the electric field produced by a distribution of charges given by the volume charge density $\rho (\vec r)$ is obtained by a triple integral of a vector function:
  • Points $\mathbf{x}$ and $\mathbf{r}$, with $\mathbf{r}$ contained in the distributed mass (gray) and differential mass $dm(\mathbf{r})$  located at the point $\mathbf{r}$.

• Triple Integrals in Spherical Coordinates

  • In $R^3$ some domains have a spherical symmetry, so it's possible to specify the coordinates of every point of the integration region by two angles and one distance.
  • Points on $z$-axis do not have a precise characterization in spherical coordinates, so $\theta$ can vary from $0$ to $2 \pi$.

• Catalytic Hydrogenation

  • A carbon-carbon triple bond may be located at any unbranched site within a carbon chain or at the end of a chain, in which case it is called terminal.
  • Since the most common chemical transformation of a carbon-carbon double bond is an addition reaction, we might expect the same to be true for carbon-carbon triple bonds.
  • Similarly, a triple bond is stronger than a double bond, but not 50% stronger.
  • However, careful hydrogenation of an alkyne proceeds exclusively to the alkene until the former is consumed, at which point the product alkene is very rapidly hydrogenated to an alkane.
  • Consequently, reduction of triple bonds occurs selectively at a moderate rate, followed by rapid addition of hydrogen to the alkene product.