0.13 Physical properties of gases  (Page 5/8)

Yet that is what we now observe for volumes and pressures of gases. We take the same syringe used in the previous experiment and trap in it a small sample of air at room temperature and atmospheric pressure. (From our observations above, it should be clear that the type of gas we use is irrelevant since the pressure and volume relationship is the same for all gases.) The experiment consists of measuring the volume of the gas sample in the syringe as we vary the sample’s temperature, which is measured by a mercury thermometer. In each measurement, the pressure of the gas is held fixed by allowing the piston in the syringe to move freely against atmospheric pressure. A sample set of data is shown in Table 3 and plotted in Figure 4.

This is an amazingly simple relationship. The volume of the gas at fixed pressure correlates exactly with the volume of the mercury in the glass cylinder, both of which correlate with the temperature. There is a simple linear (straight line) relationship between the volume of a sample of gas and its temperature. We can express this in the form of an equation for a line:

V = α t + β

where V is the volume and t is the temperature in °C. Α and Β are the slope and y-intercept of the line, respectively. For this sample of gas at this temperature, our measurements give us Α = 0.335 mL/°C and Β = 91.7 mL.

These numbers alone don’t mean much to us, because these are the specific numbers for a specific amount of gas at a specific pressure. But we can rewrite this equation in a slightly different form:

V = α (t + β/α)

This is the same equation, except that it reveals that the quantity β/α must be a temperature, since we can add it to a temperature and it has units of temperature. If we extrapolated the straight line in Figure 4 all the way to the x-axis, we find that the x-intercept of the graph, or the quantity -β/α equals -273 °C. At that temperature, the volume of the gas would be expected to be zero. This assumes that the equation can be extrapolated to that temperature. This is quite an overly optimistic extrapolation, since we haven’t made any measurements anywhere near to -273 °C. In fact, our gas sample would condense to a liquid or solid before we ever reached that low of a temperature.

We know that the volume of a gas sample depends on the pressure and the amount of gas in the sample. This means that the values of α and β also depend on the pressure and amount of gas and carry no particular significance. However, when we repeat our observations for many values of the amount of gas and many values of the fixed pressure, we find a wonderful result: the ratio -β/α = -273 °C does not vary from one sample to the next. Every set of observations produces a graph like Figure 4 with a straight line that extrapolates to an x-intercept of -273 °C.

Although we do not yet know the physical significance of this exact temperature, we can assert that it is a true constant, independent of any choice of the conditions of the experiment. We refer to this temperature as “absolute zero,” since a temperature below this value would be predicted to produce a negative gas volume. Evidently, then, we cannot expect to lower the temperature of any gas below -273 °C.