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Extra resources for Elements of Physical Chemistry (5th Edition)
In terms of 17 18 CHAPTER 1: THE PROPERTIES OF GASES the thermodynamic temperature, therefore, Charles’s law takes the simpler form Charles’s law: at constant pressure, V ∝ T It follows that doubling the temperature (such as from 300 K to 600 K, corresponding to an increase from 27°C to 327°C) doubles the volume, provided the pressure remains the same. 2 is consistent with Charles’s law. First, we rearrange it into V = nRT/p, and then note that when the amount n and the pressure p are both constant, we can write V ∝ T, as required.
Boyle’s law implies that if we compress (reduce the volume of) a ﬁxed amount of gas at constant temperature into half its original volume, then its pressure will double. 15 Temperature, θθ/°C Fig. 1 The volume of a gas decreases as the pressure on it is increased. For a sample that obeys Boyle’s law and that is kept at constant temperature, the graph showing the dependence is a hyperbola, as shown here. Each curve corresponds to a single temperature, and hence is an isotherm. The isotherms are hyperbolas, graphs of xy = constant, or y = constant/x (see Appendix 2).
Indeed, an important component of science as a whole is its technique of proposing a qualitative model and then expressing that model mathematically. The ‘kinetic model’ (or the ‘kinetic molecular theory’, KMT) of gases is an excellent example of this procedure: the model is very simple, and the quantitative prediction (the perfect gas law) is experimentally veriﬁable. The kinetic model of gases is based on three assumptions: 1. A gas consists of molecules in ceaseless random motion. 2. The size of the molecules is negligible in the sense that their diameters are much smaller than the average distance travelled between collisions.