Volume and pressure, changes

Above the critical pressure, a transformation is initiated, but, unlike isothermal equilibrium transitions, a finite pressure and volume change is typically required to complete the transition. Such a behavior is clear evidence for nonequilibrium behavior. 

Corollary. dVJ is a perfect differential when the pressure is constant, and Qi is independent of the path. The independence of the heat effect on the path requires that the change shall occur either at constant volume or at constant pressure. If the volume is maintained constant (dv = 6) the pressure may be changed in any way if the pressure is maintained constant (dp = o) the volume may be altered in any manner so that the limiting conditions are satisfied but if both pressure and volume change... 

SOLUTION We expect the final pressure, P2, to be higher than the initial pressure, Pt, because the volume occupied by the air has been decreased. Follow the second procedure in Toolbox 4.1. Only the pressure and volume change, so all other variables cancel, resulting in Boyle s law. 

For the closed valve case (C0NFL02), repeat the changes of Exercise 1, observing also the variation in the gas pressure and volume. Change the gas volume, and note the influence of this variable. 

As can be clearly seen in this figure, the gray area represents the work done in this specific process. It is also much different from paths 1 and 2. Clearly, the amount of work in a given process is highly dependent on how the pressure and volume change. For changing volume and/or pressure of a gas, the work is equal to the area under the curve describing the process. 

Since pressure and volume change, you know that the temperature of the nitrogen will also change. 

To find the new temperature based on both pressure and volume changes, you can multiply the initial temperature by... 

The basic assumption we make when using the ideal gas law to describe a change in state for a gas is that the equation applies equally well to both the initial and the final states. In dealing with a change in state, we always place the variables on one side of the equals sign and the constants on the other. In this case the pressure and volume change, while the temperature and the number of moles remain constant (as does R, by definition). Thus we write the ideal gas law as... 

This form of Boyle s Law is useful for calculations involving pressure and volume changes, as the following examples demonstrate. 

In Fig. 9 the pressure-volume relations of a gas-liquid system are represented. A corresponds to a dilute unsaturated vapour. On compression at constant temperature the pressure and volume change more or less in accordance with Boyle s law and the curve AB is followed. Imagine the vapour to be tested at various points by being placed in contact with a continuous surface of its liquid. Up to B, the saturation point, it would take up liquid which would evaporate into it. At B there would be equilibrium, and if in presence of the liquid the pressure were infinitesimally raised, complete condensation would occur at constant pressure the line BC would be followed to the point C. If pressure were raised further, the compression curve of the liquid, CD, would be traversed. The only variable... 

Gas laws discovered by Robert Boyle and Jacques Charles led to the development of the combined gas law. This law allows calculations to be made that relate temperature, pressure, and volume changes for gases. 

Note 3.6 (Notation of pressure and volume change for fluid and thermodynamic functions). Most textbooks on thermodynamics (de Groot and Mazur 1962 Kestin 1979 Kondepudi and Prigogine 1998) contain treatments of the perfect gas, therefore we have [Pg.100]

It is important to ensure that temperature is kept constant during these reactions so that pressure and volume changes are not, in part, due to temperature changes. 

Clapeyron Benoit Pierre Emile (1799-1864) Fr. eng., mathemat. theory of elasticity of solids, found relation between conversion of heat, steam, pressure and volume changes, help construction of locomotives... 

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