Experiment: Thermodynamics of Real Gases Chemistry 311L
(Heat Capacity Ratio and the Joule-Thomson Effect)
question: Imagine that you forget that an oil manometer measures pressures above atmospheric. What will happen to your calculated heat capacity ratios, and why?
To understand what will happen to the calculated heat capacity ratios, let's first understand how an oil manometer works and how it relates to atmospheric pressure.
An oil manometer is a device used to measure pressure differences. It consists of a U-shaped tube partially filled with a liquid (usually oil) and connected to the system being measured. The height difference of the liquid in the two arms of the U-tube corresponds to the pressure difference.
In the case of an oil manometer, the liquid (oil) is denser than the gas being measured. When the gas pressure is higher than atmospheric pressure, it pushes the oil down in one arm causing it to rise in the other arm. In this setup, the pressure measured is the difference between the gas pressure and atmospheric pressure.
Now, let's consider what happens when you forget that the oil manometer measures pressures above atmospheric pressure.
If you mistakenly assume that the pressure measurement from the oil manometer is the absolute pressure (without considering the atmospheric pressure), your calculated pressure values will be higher than the actual values. Remember, a pressure measurement above atmospheric pressure represents the excess pressure above the atmospheric level.
Heat capacity ratios, commonly denoted as γ (gamma), are calculated by dividing the molar heat capacity at constant pressure (Cp) by the molar heat capacity at constant volume (Cv). These ratios are affected by changes in pressure.
By mistakenly assuming that the pressure measurements from the oil manometer are absolute pressures, you will wrongly estimate the gas pressure. Consequently, your calculated heat capacity ratios will be higher than they should be.
The heat capacity ratios depend on the gas properties, and the molar heat capacities are affected by pressure changes. Thus, erroneous pressure measurements will lead to inaccurate calculations of the heat capacity ratios.
In summary, forgetting that the oil manometer measures pressures above atmospheric pressure will result in overestimating the gas pressure and, subsequently, overestimating the calculated heat capacity ratios.