Thermal Expansion of Liquids and Solids

the internal energy is just three-halves times N times Boltzmann constant times the temperature. What this means is that the degrees of freedom matter when it comes to the internal energy of a gas. Each degree of freedom contributes one-half times the Boltzmann constant times Temperature.

So, what is Boltzmann constant? Without getting into the specifics of how this is calculated, you need to know that this is the gas constant R divided by Avogadro’s number (which is the number of atoms in a mole of a substance). Boltzmann constant equals 1.38 × 10-23 kilogram-meters squared per second squared per degree Kelvin or Joules per degree Kelvin.

The average kinetic energy of a molecule is independent of the type of molecule. The average translational kinetic energy depends only on the absolute temperature (multiplied by a constant). This kinetic energy is very small when you think of its macroscopic energies so that one does not feel the collision of air molecules on the skin, just the total macroscopic pressure.

The root-mean-square velocity of a molecule is the square root of the sums of the velocities squared of the velocities in all three axes. The mean free path, which is the distance a molecule can move on average between collisions of molecules, is very small. The faster the root mean velocity of air molecules, the faster that sound vibrations can be transferred through the air. The speed of sound increases with the temperature and is greater in gases that have smaller molecules. This is why people sound differently when inhaling helium.

THERMAL EXPANSION OF LIQUIDS AND SOLIDS

Thermal expansion of gases is obvious but you need to know that solids and liquids expand with greater temperature. Raising the temperature of the gas in a balloon will increase its buoyant force or upward force. Alcohol will expand in an alcohol thermometer. Bridges and railroad tracks will have expansion joints that allow them to expand freely in higher temperatures and contract freely in lower temperatures. Thermal expansion depends on the substance as well as the actual temperature.

An increase in temperature means there is an increase in kinetic energy of the atoms. Solids are packed together but their molecules will push against one another, resulting in a slightly greater distance between neighboring molecules, adding to the size of the whole body. It will increase the solid’s size by a certain fraction in each dimension.

One can conceive of linear thermal expansion, which is thermal expansion in one direction or dimension. In such cases, the change in linear length is equal to the length multiplied by the change in temperature multiplied by the coefficient of linear expansion, which will itself vary with temperature somewhat and will vary with the substance. Nevertheless, the coefficient of linear expansion is accurate for small changes in temperature and, over large changes in temperature, an average value of this coefficient can be used.

While it is nice to look at the linear expansion of a bridge, for example, you need to know that solids and liquids expand in all dimensions. The areas and volumes will increase with temperature and holes in a solid will get larger with temperature because molecules around the hole will get further apart. In two dimensions, the change in area will be the original area, twice the coefficient of linear expansion, and the change in temperature.

As you can imagine, there is thermal expansion in all three dimensions. In such cases, the change in volume equals the coefficient of volume expansion times the original volume times the change in temperature. This introduces the coefficient of volume expansion, which is equal to approximately three times the coefficient of linear expansion. This value will vary with the type of substance.

Objects will contract with decreasing temperature but you need to know that this is not completely the case with water. Water actually expands with increasing temperature as long as the temperature is greater than 4 degrees Celsius. Between 0 and 4 degrees Celsius, water expands with decreasing temperature so that is why ice floats on water. Ice is less dense than liquid water. Water is densest at 4 degrees Celsius. As a pond cools, the colder water will drop and warmer water on top will cool until there is a uniform temperature of 4 degrees. This leads to freezing of the top layers of water that stays at the top.