Pressure-volume work, examples

In chemical applications, the most common type of work is pressure-volume work. Examples are shown in Figure 9.5. The top frame illustrates how the evolution of a gas (H2) in a spontaneous process is used to do PV work in a system... 

In the example of pressure-volume work in die previous section, the adiabatic reversible process consisted simply of the sufficiently slow motion of an adiabatic wall as a result of an infinitesimal pressure difference. The work done on the system during an infinitesimal reversible change in volume is then -pdVand one can write equation (A2.1.11) in the fomi... 

If there are other kinds of work, similar expressions apply. For example, with electromagnetic work (equation (A2.1.8)1 instead of pressure-volume work, one can write for the Helmholtz free energy... 

Most chemists perform experiments in which the contents of our beaker, flask or apparatus are open to the air - obvious examples include titrations and refluxes, as well as the kinetic and electrochemical systems we consider in later chapters. The pressure is the air pressure (usually pe), which does not change, so any pressure-volume work is the work necessary to push back the atmosphere. For most purposes, we can say w = pAV. 

For many systems, the non-pressure-volume work term, Vynon.PV is generally used (see Section 3.2 for surface area expansion) and we need to consider other ways that work can be done on a body. The rate at which work is done is always of the form dW = P dx where dx is an extensive property and represents the change in the extent of some quantity, and P is a force that resists this change. This should be familiar from, for example, springs and... 

The work involved in the expansion or compression of gases is called pressure-volume work (or P-Vwork). When pressure is constant in a process, as in our preceding example, the sign and magnitude of the pressure-volume work are given by... 

The only type of work involved in most chemical and physical changes is pressure-volume work. From dimensional analysis we can see that the product of pressure and volume is work. Pressure is the force exerted per unit area, where area is distance squared, d volume is distance cubed, i Thus, the product of pressure and volume is force times distance, which is work. An example of a physical change (a phase change) in which the system expands and thus does work as it absorbs heat is shown in Figure 15-6. Even if the book had not been present, the expanding system pushing against the atmosphere would have done work for the expansion. 

What is the purpose of a thermodynamic and stochastic theory of hydrodynamics The thermodynamic potential (state) functions for irreversible processes approaching equilibrium are known, for example the Gibbs free energy change for a process at constant temperature and pressure. Changes in that energy yield the maximum work, other than pressure volume work, available from that process. Then, by analogy, the aims of a theory of thermodynamics for hydrodynamics are the establishment of evolution criteria... 

Gaseous systems are useful examples for thermodynamics because we can use various gas laws to help us calculate the amount of pressure-volume work when a system changes volume. This is especially so for reversible changes, because most reversible changes occur by letting the external pressure equal the internal pressure ... 

EXAMPLE 6.4 Pressure-Volume Work To inflate a balloon you must do pressure-volume work on the surroundings. If you inflate a balloon from a volume of 0.100 L to 1.85 L against an external pressure of 1.00 atm, how much work is done (in joules) ... 

We calculated the amount of work done by the gas in a single-stage expansion in Example 7-5 it was u> = -1.24 X 10 J. The amount of work done in the two-stage process is the sum of two terms the pressure-volume work for each stage of the expansion. 

This example is also used as a worked example for level swell calculations in A3.3.6. A reactor of volume 3.6 m3 contains 2610 kg of reactants under worst case runaway conditions. The relief pressure is 5.5 bara and the maximum accumulated pressure is 7.0 bara. 

A system can do two kinds of work. The first type is expansion work, which involves a change in volume of the system against an external pressure. For example, a gas expanding in a balloon pushes out against the atmosphere and thus does work on it. The second type of work is nonexpansion work, work that does not involve a change in volume. For example, a chemical reaction can do work by causing an electrical current to flow, and our bodies do work by moving about. 

Now suppose that the walls are movable, so the system can expand when the reaction takes place. At this stage, let s suppose that the external pressure is constant. A gas confined by a piston that is free to move against an external pressure is an example of such a system (Fig. 6.8). The external pressure acting on the outer face of the piston provides the force opposing expansion, and we can suspect that the amount of work done when the system expands through a volume AV is proportional to the external pressure Pex. Now we need to find the quantitative relation between the work and the external pressure. 

Still other applications of the ideal gas law make it possible to calculate such properties as density and molar mass. Densities are calculated by weighing a known volume of a gas at a known temperature and pressure, as shown in Figure 9.10. Using the ideal gas law to find the volume at STP and then dividing the measured mass by the volume gives the density at STP. Worked Example 9.7 gives a sample calculation. 

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