Piston, expansion work done

First, we consider the expansion work done by a system consisting of a gas in a cylinder. The external pressure acting on the outer face of the piston provides the force opposing expansion. We shall suppose that the external pressure is constant, as when the piston is pressed on by the atmosphere (Fig. 6.5). We need to find how the work done when the system expands through a volume AV is related to the external pressure Pcx. 

FIGURE 6.10 The expansion of a gas against a constant external pressure (such as atmospheric pressure). The gas is in a cylinder fitted with a weightless movable piston. The work done is given by —PAV. 

If the piston is well-lubricated and well-constructed, we can ignore friction effects, and the pressure-volume history of the change can be illustrated as in Figure 4.7. The external pressure during expansion is constant, since it is fixed by the mass of the piston. The work done during the expansion is ... 

Thus, we expect the spontaneous expansion of a gas to result in an increase in entropy. To see how this entropy increase can be calculated, consider the expansion of an ideal gas that is initially constrained by a piston, as in the rightmost part of Figure 19.5. Imagine that we allow the gas to undergo a reversible isothermal expansion by infinitesimally decreasing the external pressure on the piston. The work done on the surroimdings by the reversible expansion of the system against the piston can be calculated with the aid of calculus (we do not show the derivation) ... 

If a fluid contained in a cylinder expands so that its pressure remains constant (e.g.9 saturated steam in contact with water), the work done is that of raising the piston, of area a, which supports a weight W just sufficient to keep the expansive force indefinitely near equilibrium. If s = distance of outward motion of piston work A = W. s = pa. s = p. as = p v, where Av is the increase of volume. 

M FIGURE 8.4 The expansion in volume that occurs during a reaction forces the piston outward against atmospheric pressure P. The amount of work done is equal to the pressure exerted in moving the piston (the opposite of atmospheric pressure, — P) times the volume change (AV). The volume change is equal to the area of the piston (A) times the distance the piston moves (d). Thus, w = —PAV. 

A short calculation gives the exact amount of work done during the expansion. We know from physics that force (F) is defined as area times pressure. In Figure 8.4, the force that the expanding gas exerts is the area of the piston (A) times the pressure with which the gas pushes against the piston. This pressure is equal in magnitude but opposite in sign to the external atmospheric pressure (P) that opposes the movement, so it has the value -P. 

We return to the piston-and-cylinder arrangement discussed in Section 2.3. In that discussion we did not completely describe the process because we were interested only in developing the concept of work. Here, to complete the description, we choose an isothermal process and a gas to be the fluid. We then have a gas confined in the piston-and-cylinder arrangement. A work reservoir is used to exert the external force, Fe, on the piston this reservoir can have work done on it by the expansion of the gas or it can do work by compressing the gas. A heat reservoir is used to make the process isothermal. The piston is considered as part of the surroundings, so the lower surface of the piston constitutes part of the boundary between the system and its surroundings. Thus, the piston, the cylinder, and the two reservoirs constitute the surroundings. 

A common type of work associated with chemical processes is work done by a gas (through expansion) or work done to a gas (through compression). For example, in an automobile engine the heat from the combustion of the gasoline expands the gases in the cylinder, pushing back the piston. This motion is then translated into the motion of the car. 

Let us change our system to include the gas, the piston, and the cylinder. With this choice, the system expansion is still irreversible, but the pressure in the surroundings can be assumed to be atmospheric pressure and is constant. The work done in pushing back the atmosphere probably is done almost reversibly from the viewpoint of the surroundings and can be closely estimated by calculating the work done on the surroundings ... 

We assumed in Section 3.5 that the vessel had a fixed geometry, so that no power was spent in bulk expansion. In the absence of any other power output, we could set P = 0 in equation (3.43). But if the bounded volume had one or more free surfaces (e.g. a inside a piston chamber, or above a liquid in a vessel with a gas over-blanket), then we would need to take account of the work done against the imposed pressure. Let us take the case where the top surface in Figure 3.2 moves up a small amount in the time interval St, so that the volume of the fluid increases by an amount (m ). Assuming that the pressure above this surface is p, (Pa), the work done is given by ... 

Suppose that water at its normal boiling point (100 C or 73 K) is maintained in a cylinder that has a frictionless piston. The equilibrium pressure of the vapor will be 1 atm, and an external pressure of 1 atm must therefore be exerted on the piston in order to prevent it from moving. Suppose that we now reduce the external pressure by an infinitesimal amount in order to have a reversible expansion. We allow the piston to sweep out a volume of 2 dm, and want to calculate the work done by the system. 

Tlie work done by gases occurs during the expansion stroke. Mechanical systems used today make compression equal to the expansion stroke. It is possible to avoid this combination by using a special cam profile adjustment along with the well known Miler principle. If, during the first part of the upward movement of the piston you maintain the admission valve open, you are in fact reducing the compression stroke. Mazda is said to be marketing such a solution soon (fig. 12). 

Figure 7.2 illustrates the mechanical work involved in the expansion (or compression) of a gas. Suppose that a gas is in a cylinder fitted with a weightless, frictionless movable piston, at a certain tanperature, pressure, and volume. As it expands, the gas pushes the piston upward a distance Ax against a constant opposing external atmospheric pressure which is defined as the external force F per unit area A (Equation 5.1). Using Equation 0.2, the work done on the gas by the piston is... 

In an isothermal process, the temperature remains a constant during the entire operation. Consider an ideal gas contained in a cylinder fitted with a frictionless weightless piston placed in a thermostat. Let the pressure of the gas be P. During expansion let the external pressure be reduced by a very small quantity dP and let the volume change during reversible expansion be dV. The work done, w by the gas in the reversible expansion is given by... 

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