Volume relationship with pressure

Charles and Gay-Lussac, working independently, found that gas pressure varied with the absolute temperature. If the volume was maintained constant, the pressure would vary in proportion to the absolute temperature [I j. Using a proportionality constant R, the relationships can be combined to form the equation of state for a perfect gas, otherwi.se known as the perfect gas law. 

For a calculation of d. see R- H. Fowler. Statistical Thermodynamics. Second Edition, Cambridge University Press. 1956. p. 127. In Section 1.5a of Chapter 1 we defined the compressibility and cautioned that this compressibility can be applied rigorously only for gases, liquids, and isotropic solids. For anisotropic solids where the effect of pressure on the volume would not be the same in the three perpendicular directions, more sophisticated relationships are required. Poisson s ratio is the ratio of the strain of the transverse contraction to the strain of the parallel elongation when a rod is stretched by forces applied at the end of the rod in parallel with its axis. 

The body s normal daily sodium requirement is 1.0 to 1.5 mEq/kg (80 to 130 mEq, which is 80 to 130 mmol) to maintain a normal serum sodium concentration of 136 to 145 mEq/L (136 to 145 mmol/L).15 Sodium is the predominant cation of the ECF and largely determines ECF volume. Sodium is also the primary factor in establishing the osmotic pressure relationship between the ICF and ECF. All body fluids are in osmotic equilibrium and changes in serum sodium concentration are associated with shifts of water into and out of body fluid compartments. When sodium is added to the intravascular fluid compartment, fluid is pulled intravascularly from the interstitial fluid and the ICF until osmotic balance is restored. As such, a patient s measured sodium level should not be viewed as an index of sodium need because this parameter reflects the balance between total body sodium content and TBW. Disturbances in the sodium level most often represent disturbances of TBW. Sodium imbalances cannot be properly assessed without first assessing the body fluid status. 

The analogue to one-component thermodynamics applies to the nature of the variables. So Ay S, U and V are all extensive variables, i.e. they depend on the size of the system. The intensive variables are n and T -these are local properties independent of the mass of the material. The relationship between the osmotic pressure and the rate of change of Helmholtz free energy with volume is an important one. The volume of the system, while a useful quantity, is not the usual manner in which colloidal systems are handled. The concentration or volume fraction is usually used ... 

Generally, the higher the pressure, the higher is the solubility of a gas in a liquid. This relationship is expressed quantitatively by Henry s Law which states that the mass of gas (m) dissolved by a given volume of solvent at a constant temperature is proportional to the gas pressure (p) with which it is in equilibrium ... 

The universe as a whole is made up of material with three distinct states, namely the solid state, the liquid state and the gaseous state. In 1662, Robert Boyle showed for the first time the relationship between volume and pressure of a gas under constant temperature to be inverse proportional to one another. In 1802 Gay-Lussac reported his discovery on the relationship between the volume of gas and temperature under constant pressure to be proportional to one another. These two relationships laid the foundation for the equation of state for gaseous state namely,... 

The curve shown in Fig. 22, for an R100 impeller illustrates that there is a break point in the relationship with KGa versus the power level at the point where the power of the mixer is approximately three times the power in the expanding gas stream. The power per unit volume for an expanding gas stream at pressures from 1 to 100 psi can be expressed by the equation P/V (HP/1000 gal) = 15F (ft/sec). The A315 impeller, Fig. 23, is able to visually disperse gas to a ratio of about 1 to 1 in expanding gas power and mixer power level. It does not have a break point in the curve, although slopes are somewhat different than those in Fig. 22. 

The effect of substances on the compliance of the bladder wall is evaluated by comparing the volume-pressure-relationship of treated animals with that of controls. 

In this section, you learned about the relationship between volume and temperature (Charles law). You also learned about the relationship between pressure and temperature (Gay-Lussac s law). In the next section, you will see how these relationships can be combined with Boyle s law to produce one equation that works in all three situations. 

The reduced density, temperature, and pressure along with the characteristic temperature, pressure, and volume are calculated from the following relationships. 

This is an inverse relationship, meaning that as pressure increases, the volume decreases, and as pressure decreases, volume increases. These relationships are true when the temperature and number of molecules are held constant Again, this fits with what you observed in the simulation. 

What we need at this point is another relationship relating these same parameters. One such relationship is called an equation of state (EOS). The EOS gives all of the equilibrium states in which a material can exist and is written in terms of specific internal energy, pressure, and specific volume. We do not have a general EOS that can be derived for all materials. There is, of course, the ideal gas equation, PV = nRT, where RT is related to the specific internal energy, but we are not dealing with ideal gases here. Our main interest is in solids. But if there were such an EOS,... 

Dilute solutions. As has already been stated (p. 266), the relationship between the osmotic pressure of a solution and the concentration and chemical character of solvent and solute cannot be derived from purely thermodynamical considerations. There are several ways of attaining this end. In the first instance, the variation of the osmotic pressure with the concentration can be determined experimentally, and the results embodied in an empirical equation of the form p=/(c). Or we may deduce relationships from kinetic conceptions of the nature of solutions, in much the same way as the gas laws were deduced. Or, finally, we may deduce the osmotic pressure laws, with the aid of the thermodynamical equations of the previous paragraph, from empirical or theoretical researches on the vapour pressure of solutions. These methods all lead to the same result, that the osmotic pressure of dilute solutions obeys the same laws as the pressure of a perfect gas. In other words, the osmotic pressure of a substance in solution is equal to the pressure which the substance would exert in the form of a perfect gas occupying, at the same temperature, the volume of the solution. 

Robert Boyle (1627-1691), an Irish chemist, did experiments like the one shown in Figure 14-2 to study the relationship between the pressure and the volume of a gas. By taking careful quantitative measurements, he showed that if the temperature is constant, doubling the pressure of a fixed amount of gas decreases its volume by one-half. On the other hand, reducing the pressure by half results in a doubling of the volume. A relationship in which one variable increases as the other variable decreases is referred to as an inversely proportional relationship. For help with understanding inverse relationships, see the Math Handbook page 905. 

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 ... 

How are gas temperature and volume related The French physicist Jacques Charles (1746-1823) studied the relationship between volume and temperature. In his experiments, he observed that as temperature increases, so does the volume of a gas sample when the pressure is held constant. This property can be explained by the kinetic-molecular theory at a higher temperature, gas particles move faster, striking each other and the walls of their container more frequently and with greater force. For the pressure to stay constant, volume must increase so that the particles have farther to travel before striking the walls. Having to travel farther decreases the frequency with which the particles strike the walls of the container. 

An example of a typical direct relationship is the increase in volume of a gas with increasing temperature. When the gases inside a hot air balloon are heated, the halloon gets larger. As the balloon cools, its size decreases. However, a plot of the decrease in pressure as the volume of a gas increases yields a typical inverse curve. 

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