Absolute Zero

In this experiment, my goal was to find the temperature of absolute zero. To do this I heated a beaker to 70°C, in a vat of water, and then placed a cork in the beaker. Running through this beaker was a piece of tubing attached to a pressure gage. The pressure gage was simply a U of glass tubing, filled with mercury, held up on a stand. One end of the U was attached to the tube coming from the beaker; the other end was open to the atmosphere. Therefore, the measurements I would be making would be mm of mercury difference between the pressure inside the beaker and pressure outside the beaker. Later, I could correct the measurements to pascals. As the temperature of the water the beaker was submerged in dropped so too did the pressure inside the beaker. This can easy be explained by looking at the ideal gas equation (Equation 1). Because the beaker is sealed the volume and number of moles of gas cannot change, and the molar gas constant is a constant so it cannot change. Therefore, the only thing that can change when the temperature is lowered is the pressure.

Equation 1. This is the ideal gas equation. It functions only if the molecules have elastic collisions. P = pressure in pascals. V = the volume the gas is takes up.  n = the number of moles of gas that are present. R = the molar gas constant (≈8.3145 J/(mol K)). T = the temperature in Kelvin.

I took temperature and pressure readings about every 5 to 8 degrees of temperature change (Table 1). I then converted the mm of mercury to pascals by finding out how many pascals it took to move the mercury one mm (1mm of mercury = 133.322368 pascals), multiplying the number of mm by the number of pascals per mm. This only gave me the pressure differences. To find actual pressure in the beaker I subtracted the difference from the pressure in the room (99,700pa). I then plotted the data points on a graph (Figure1) and fitted a trend line to it, using Excel trend line. To find absolute zero I had to find the point at which the pressure was equal to zero. The reason behind this is at absolute zero all motion of molecules stops, and if the molecules are not moving, there is no way of them exerting pressure. Therefore, at absolute zero there is zero pressure. Figure 1 is a graph that plots pressure vs temperature. It is a graph that I fit a trend line to and used it to find the temperature of absolute zero.

Figure 1. This graph shows all of the data I collected on the run from 70°C to 0°C. Excel fit the trend line.

After solving for temperature when the pressure is zero I found absolute zero to be -668 °C . The real temperature of absolute zero is -273.15°C.  I was off by about 5°C and I was amazed by how close to the real number I got.

I did a second run of the experiment, this time using liquid nitrogen to cool down the beaker. I was able to get the gas inside the beaker to -100°C. However, the data I collected for this run was not very good. The reason for this was the liquid nitrogen cooled the beaker so fast it was difficult to get accurate simultaneous temperature and pressure measurements. This can be seen by looking at the plot of the data in Figure 2. I fitted a trend line to the data and got a temperature for absolute zero of -218°C. By looking at Figure 2 you can understand why the trend line is so off, the data was not as linear as in the first run.

Figure 2. This graph shows all of the data I collected on the run from 20°C to -100°C. The trend line was fitted by Excel.

Over all this was a really cool experiment.  It was simple but you could find some really interesting data with it. Being able to find the temperature of absolute zero after three hours in the lab was awesome.

-Kyle