Boyle inversion curve

The extrapolation behaviour of empirical multi-parameter equations of state has been summarized by Span and Wagner. " Aside from the representation of shock tube data for the Hugoniot curve at very high temperatures and pressures, an assessment of the extrapolation behaviour of an equation of state can also be based on the so called ideal curves that were first discussed by Brown. While reference equations of state generally result in reasonable estimates for the Boyle, ideal, and Joule-Thomson inversion curves, the prediction of reasonable Joule inversion curves is still a challenge. Equations may result in unreasonable estimates of Boyle, ideal and Joule-Thomson plots especially when the equations are based on limited experimental data. 

This curve describes any inverse relationship. The commonest value for the constant, k, in anaesthetics is 1, which gives rise to a curve known as a rectangular hyperbola. The line never crosses the x or the y axis and is described as asymptotic to them (see definition below). Boyle s law is a good example (volume = 1/pressure). This curve looks very similar to an exponential decline but they are entirely different in mathematical terms so be sure about which one you are describing. 

Boyle s law states that the volume of a given amount of gas held at a constant temperature varies inversely with the pressure. Look at the graph in Figure 14-2 in which pressure versus volume is plotted for a gas. The plot of an inversely proportional relationship results in a downward curve. If you choose any two points along the curve and multiply the pressure times the volume at each point, how do your two answers compare Note that the product of the pressure and the volume for each of points 1, 2, and 3 is 10 atm-L. From the graph, what would the volume be if the pressure is 2.5 atm What would the pressure be if the volume is 2 L ... 

When the volume of a gas is plotted against its pressure at constant temperature, the resulting curve is one branch of a hyperbola. Figure 12-4b is a graphic illustration of this inverse relationship. When volume is plotted versus the reciprocal of the pressure, /P, a straight line results (Figure 12-4c). In 1662, Boyle summarized the results of his experiments on various samples of gases in an alternative statement of Boyle s Law ... 

It is convenient to represent the data in Table 5.1 by using two different plots. The first type of plot, P versus V, forms a curve called a hyperbola shown in Fig. 5.5(a). Looking at this plot, note that as the volume drops by about half (from 58.8 to 29.1), the pressure doubles (from 24.0 to 48.0). In other words, there is an inverse relationship between pressure and volume. The second type of plot can be obtained by rearranging Boyle s law to give... 

Boyle s law states that the volume of a fixed amount of gas held at a constant temperature varies inversely with the pressure. Look at the graph in Figure 13.1, in which pressure versus volume is plotted for a gas. The plot of an inversely proportional relationship results in a downward curve. 

FIG. 4. Boyle s law, which established the inverse relationship of pressure and the volume of a gas at constant temperature, derived from the experiment illustrated below. Mercury dropped in long arm of tube drove the trapped air into short arm. Doubling the column of mercury halved the column of air. Relationship is plotted in the curve above, a section of one branch of the hyperbola. 

Plotting the values of volume versus pressure for a gas at constant temperature gives a curve like that in Figure 2.2. The general volume-pressure relationship that is illustrated is called Boyle s law. Boyle s law states that the volume of a fixed mass of gas varies inversely with the pressure at constant temperature. 

Note the resemblance to the ideal gas law Note also how the dotted line in Figure 22.11 mimics the hyperbolic curve of an inverse relationship between tt and A, that is, Boyle s law. In these regions, each molecule can wiggle around independently of the others, and can be modeled as a sort of two-dimensional gas. 

An example of a Cartesian coordinate system that is used extensively in physical chemistry is illustrated in Fig. 1-2. Here, the ordinate axis represents the variable pressure, while the abscissa represents the variable volume. Since both pressure and volume must be positive numbers, it is customary to omit the negative values from the coordinate system. Any curve drawn on this coordinate system represents the functional dependence of pressure on volume and vice versa. (Functions are described in Ch ter 2). For example, the curve shown in the diagram is a representation of Boyle s law, PV = k, and describes the inverse proportionality between pressure and volume for an ideal gas. The equation describing this curve on the graph... 

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