Temperature and Kinetic Theory

We need to start our lessons in thermodynamics by introducing some terms. Kinetic Theory is the theory that matter is made up of atoms, and that these atoms are always in motion. In fact, this supposition that atoms make up all matter is important to our understanding of what thermodynamics is all about. I mention this because we are going to use the motion of molecules to explain what temperature is and how heat is transferred from one substance to another. Molecules are always in motion. This was noticed by the botanist Robert Brown, who saw that pollen was moving around in a solution even though the solution was not being disturbed. This movement was called Brownian Motion, (Click here for an applet on Brownian Motion) and it was further expounded upon by Einstein when he wrote a paper on it in 1905. (A digression: 1905 was an incredible year for Einstein - his "Annus Mirabilis" when he produced five ground-breaking papers while working as a third-class clerk in the Swiss Patent Office. The five papers were:

But we digress enough. Here are some definitions and explanations that we are going to come across in our discussions. Let's just get them out of the way right now.

  • The Unified Atomic Mass Unit (u) is used to show the molecular or atomic mass of substances and compounds. It is based on Carbon-12, where the mass is exactly 12.000000u. 1u = 1.66 x 10-27 kg.
  • Temperature is a measure of how "hot" or "cold" something is. These are actually relative terms. Boiling
    water is hot compared to ice, but cold compared to the temperature of the sun's surface. The instrument we use to measure temperature is the Thermometer. Most thermometers rely on some characteristic of thermal expansion in order to function.

The scales we use are Centigrade, Kelvin, and Fahrenheit. Centigrade is the most common, and we will use it almost exclusively in our course. The Kelvin system is the absolute measurement system. Fahrenheit is used commonly in the US for non-engineering or scientific measurements. There are other scales, such as the
Rankine scale, but they are far less commonly used.

 

  The relationship between C and K: A change of 1oC is also a change of 1oK.

0
OK (absolute zero) = -273.15 oC.

The relationship between C and F: This is a little more complex. The freezing point of water is 0 oC or 32 oF.
The boiling point of water is 100 oC or 212 oF. Two formulas provide a conversion:

T (oC) = 5/9 (T(oF)
- 32) or T (oF) = 9/5 (T (oC) + 32

What are some things that change with temperature? Size, resistivity, color, state, and motion are just a few of
the things that we'll take a look at.

  • Thermal Equilibrium:
    When two objects with different temperatures are placed in contact such that thermal energy can be exchanged, then they will eventually both reach the same temperature. Heat will "flow" to the cooler object until both are in equilibrium. When there is no energy transfer between them, there is no corresponding change in temperature. Finally, when two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. This is the "Zeroth law of thermodynamics."
  • Thermal Expansion:
    Generally, as things heat up or cool down, they expand or contract. (An exception to this that we noted is the behavior of water between 0oC and 4 oC). This is a nice thing to know when we are designing
    bridges, roads, towers, tanks, and other objects that are likely to expand or contract with daily changes in temperature. We picked up some terms and formulas to help describe how these change.

a - Coefficient of Linear Expansion

b - Coefficient of Volume Expansion

The units of both are oC-1

Lo = Initial Length, Vo = Initial Volume, DT = Change in Temperature, so:

DL = aLoDT and DV = bVoDT

and as a good approximation, b =3a

Note:

  1. The coefficients of linear and of volume expansion depend only on the material the object is made from.
  2. The length of an object undergoing thermal expansion changes by an amount proportional to the original length and the change in temperature.

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For even more on Brownian Motion, try http://www.exploratorium.edu/xref/phenomena/brownian_motion.html For more on thermal expansion, try http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thexp.html And for more on Thermal Equilibrium, try http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html 

For Practice Problems, Try:

Temperature Conversion

Thermal Expansion

Volumetric Expansion

Giancoli Multiple Choice Practice Questions (Questions 1-15)