Measurement of Heat Capacity Ratio and Speed of Sound in Gases
September 12, 2013
Physical Chemistry Laboratory
The speed of sound in gases will be studied by two types of tests on four gases: argon, carbon dioxide, helium, and dry air. The two tests that will be used on different settings on an oscilloscope are: the X-Y mode and internal time base mode. The gases will be filtered through a tube that is connected to an acoustical tube with a microphone and earpiece. The different waves will be displayed through a screen on the oscilloscope where the wavelength can be determined by studying the different patterns. Once the wavelength is calculated, the heat capacity ratio for each of the gases will be calculated.
When temperature is increased in a system, the internal energy is raised. It is assumed that the system has a constant volume, so the increase depends on different conditions based on which the heating takes place. If internal energy is plotted against temperature, a curve can be seen in a graph. The graph shows a variation as the system heats at a constant volume. The slope of the tangent line to the curve is called the heat capacity at a certain temperature at a constant volume. CV denotes the heat capacity at a constant volume. The equation is as follows:
CV is the derivative of the internal energy in respect to temperature. The equipartition theorem says that each term in the total energy expression with either a squared momentum or coordinate contributes the same amount, (1/2)RT to the energy as well as the heat capacity. 
Heat capacity ratio is a quantity that appears frequently. It is the ratio of CP to CV, which is defined by ϒ. This value for gas reflects different characteristics of a gas. It can also be known if Cp or Cv are also known. Sound is propagated through a gaseous medium by longitudinal waves. There is a connection between the speed of sound and the heat capacity ratio.