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Elementary Thermodynamics - Temperature

Temperature

In an ideal, monatomic1 gas (one atom per molecule), the mathematical relationship between average molecular velocity and temperature is as follows:

 

Where,

  m = Mass of each molecule

  v = Velocity of molecule in the sample


  = Mean-squared molecular velocities in the sample

  k = Boltzmann’s constant (1.38 × 10-23 J / K)

  T = Absolute temperature (Kelvin)

 

Non-ideal gases, liquids, and solids are more complex than this. Not only can the atoms of complex molecules move to and fro, but they may also twist and oscillate with respect to each other. No matter how complex the particular substance may be, however, the basic principle remains unchanged: temperature is an expression of how vigorously molecules are moving within a substance. There is a temperature at which all molecular motion ceases. At that temperature, the substance cannot possibly become “colder,” because there is no more motion to halt. This temperature is called absolute zero, equal to -273.15 degrees Celsius, or -459.67 degrees Fahrenheit. Two temperature scales based on this absolute zero point, Kelvin and Rankine, express temperature relative to absolute zero. A sample of freezing water at sea level, stable in temperature at 0 degrees Celsius (32 degrees Fahrenheit), is also at 273.15 Kelvin2 or 488.67 degrees Rankine.

A set of common melting and boiling points (at sea-level atmospheric pressure) appears in this table, labeled in these four different units of temperature measurement. Note how degrees Celsius and Kelvin for each point on the table differ by a constant (offset) of 273.15, while each corresponding degree Fahrenheit and degree Rankine value differs by 459.67 (note that many of the figures in this table are slightly rounded, so the offset might not be exactly that much). You might think of Kelvin as nothing more than the Celsius scale zero-shifted by 273.15 degrees, and likewise degrees Rankine as nothing more than the Fahrenheit scale zero-shifted by 459.67 degrees:


  Melting or boiling substance 
oC
oF
K oR
  Melting point of water (H2O) 
  0    32 
  273.15     491.67 
  Boiling point of water (H2O) 
  100 
  212 
  373.15 
  671.67 
  Melting point of ammonia (NH3
  -77.7 
  -107.9 
  195.5 
  351.8 
  Boiling point of ammonia (NH3
  -33.6 
  -28.5 
  239.6
  431.2 
  Melting point of gold (Au) 
  1063 
  1945 
  1336 
  2405 
  Melting point of magnesium (Mg) 
  651 
  1203.8     924.2 
  1663.5 
  Boiling point of acetone (C3H6O) 
  56.5     133.7 
  329.65     593.37 
  Boiling point of propane (C3H8
  -42.1     -43.8 
  231.1 
  415.9 
  Boiling point of ethanol (C2H6O) 
  78.4 
  173.1 
  351.6 

  632.8

 

1Helium at room temperature is a close approximation of an ideal, monatomic gas, and is often used as an example for illustrating the relationship between temperature and molecular velocity.

2Kelvin is typically expressed without the customary “degree” label, unlike the three other temperature units: (degrees) Celsius, (degrees) Fahrenheit, and (degrees) Rankine.

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