A third temperature scale has been developed, which relates the temperature changes to pressure changes for a fixed volume of gas. This scale is not based on the property of a single gas but is a result that can be obtained for any gas. The pressure was plotted vs. temperature for all the gases used. A linear calibration curve was obtained for each of the gases, which when extrapolated to lower temperatures was found to have a common intersection point for all of the curves. The common intersection point occurred at -273.15 oC. This temperature has been called Absolute Zero. Absolute zero is the temperature at which a substance has no internal energy. This new scale an absolute scale is called the Kelvin scale. In an absolute scale the value of zero is significant. There are no negative values on the Kelvin scale. A second reference point for the Kelvin scale is the triple point (combination of temperature and pressure where solid, liquid and gas can occur simultaneously at 0.01oC and 4.58 mm of Hg) of water. We can convert from Kelvin to Celsius as follows:

Thermal Expansion The Kelvin scale is based on the pressure of gases as you change the temperature. If you do not hold the volume constant, changes in pressure or temperature will cause the gases to expand or contract. Liquids and solids also expand and contract when the temperature of the object changes. As the temperature of an object increases molecules begin moving faster, increasing the average separation distance between the molecules for most materials. This causes the dimensions of the object to increase. The reverse occurs for a decrease in temperature. Examples of thermal expansion: Expansion joints used on bridges. The materials used in the bridge will expand and contract as the temperature changes throughout the year. These joints prevent the buckling of the bridge. Water Water contracts from 100oC to 4oC Water expands from 4oC to 0oC This is due to the required length of the molecular bond between different water molecules during a phase change.

We can determine the amount of thermal expansion or contraction that occurs in materials. If the thermal expansion is small compared to the initial dimensions you can approximate this change as a change in length only. DL – Change in length [m] L0 – Initial length [m] a – Coefficient of linear expansion [1/oC] DT – Change in temperature [oC] For real objects we must look at expansion in all three dimensions. aDT << 1 for temperatures less than 100oC, so we can neglect higher order terms and restrict ourselves to a max temperature of 100oC. Similarly, Volume expansion Surface area expansion