Piston-cylinder example pressure-volume

Example 2.1 A gas is confined in a cylinder by a piston. The initial pressure of the gas is 7 bar, and the volume is 0.10 m3. The piston is held in place by latches in the cylinder wall. The whole apparatus is placed in aAotal vacuum. What is the energy change of the apparatus if the retaining latches are removed so that the gas suddenly expands to double its initial volume The piston is again held by latches at the end of the process. 

Suppose, for example, that we have a gas confined in a cylinder that has a friction-less movable piston (Figure 4.1). If the piston is motionless, the state of the gas can be specified by giving the values of pressure, volume, and temperature. However, if the gas is compressed very rapidly it passes through states in which pressure and temperature cannot be specified, since these properties vary throughout the gas the gas near the piston is compressed and heated and the gas at the far end of the cylinder is not. The gas then would be said to be in a nonequilibrium state, and pure thermodynamics could not deal with such a state, although it could tell us what kind of a change would spontaneously occur in order for equilibrium to be attained. 

Example 4.4. A sample of air and coal is contained in the constant-pressure cylinder shown in Fig. 4.3. This cylinder has a frictionless, weightless piston, so the pressure inside the cylinder is always exactly the same as the pressure of the atmosphere (which we assume is 1 atm). A small spark is now introduced, causing the coal to burn. When the burning is over, Jthe piston has moved so that the volume of the contents is increased by 1 ft I The heat transferred to the surroundings was 42 Btu. What is the internal-energy change for this reaction ... 

Now imagine carrying out the same reaction in a metal cylinder with a movable piston. As this explosive decomposition proceeds, the piston in the metal cylinder will move. The gas produced in the reaction pushes the cylinder upward, thereby increasing the volume of the container and preventing any increase in pressure. This is a simple example of mechanical work done by a chemical reaction. Specifically, this type of work is known as pressure-volume, or PV, work. The amount of work done by such a process is given by... 

Example 2.10 A horizontal piston-and-cylinder arrangement is placed in a constant-temperature bath. The piston slides in the cylinder with negligible friction, and an external force holds it in place against an initial gas pressure of 14 bar. The initial gas volume is 0.03 m3. The external force on the piston is reduced gradually, allowing the gas to expand until its volume doubles. Experiment shows that under these conditions the volume of the gas is related to its pressure in such a way that the product PV is constant. Calculate the work done in moving the external force. 

Example 1.1 Equilibrium in subsystems Consider a closed isolated cylinder with two subsystems of 1 and 2 containing air with an equal volume of 1L and equal temperatures of 298.15 K. There is a fixed piston at the boundary of the subsystems, which have different pressures of Px = 2 atm and P2 1 atm. Estimate the temperature, volume, and pressure of the subsystems when the piston is released. Assume that the piston is impermeable to air, freely movable, and heat conducting. 

Volume and pressure are easy. Volume is simply the amount of space occupied by something, in this example a gas, whose volume is actually defined by its container, in this case a cylinder with a piston in one end (Figure 10-1). (You get sick of pictures of cylinders and pistons after studying thermodynamics for a while ) Pressure is simply the force exerted per unit area on the walls of the container, including the piston (P = F/A). 

Tire work wlriclr accomparries a clrange in volume of a fluid is ofteir eircountered iir thenrrodyiramics. A common example is tire compression or expansion of a fluid iir a cylinder re suiting from the movement of a piston. The force exerted by tire piston on the fluid is equal to the product of the piston area arrd tire pressure of tire fluid. The displacement of tire piston is equal to the total volume clrange of tire fluid divided by tire area of tire piston. Equation (1.1) therefore becomes ... 

A useful example of mechanical work is the expansion of a gas (Figure 6.10). Suppose that a gas is in a cylinder fitted with a weightless, frictionless movable piston, at a certain temperature, pressure, and volume. As it expands, the gas pushes the piston upward against a constant opposing external atmospheric pressure P. The work done by the gas on the surroundings is... 

A complete thermodynamic description of a material under pressure requires knowledge of the (thermal) equation of state (EOS), for example, in the form F = V (p,T) or p = p (p,T), for the specific material, where V is usually the specific volume (the volume per unit mass) or the molar volume and p is the specific density p=l/F. For a rigid cylinder with a fixed amount of a sample enclosed by the piston, the relative change in volume V(p,T)IVo is directly related to the movement of the piston if deformations of the piston and cylinder, and leakage and friction, can be neglected. For pressures below 1 GPa and moderate temperatures these techniques are well developed for liquids and gases. However, for higher pressures and variable temperatures the encapsulation of the sample and the deformation of the pressure vessel need special attention. The state of the art for encapsulated solids corresponds to a precision of only 500 p.p.m. (parts per million) in V/Vq or 3 per... 

In equilibrium, a certain extensive variable may change freely. Further, equilibrium is characterized by d 17=0, for a closed system. We will now restrict to the exchange of like energy forms. Standard exchange of an extensive variable X means that dXi = - dX2. For example, if two cylinders (1) and (2) with pistons both with equal area are connected as depicted in Fig. 6.2, then the volumes change as d Vi = —dV2. In this case, in equilibrium the pressures are equal, since... 

We imagine an example for the thermodynamic system under consideration Assume, the system is a gas in a cylinder with freely movable piston. The cylinder is isolated thermally. The environment is the atmosphere. Then the gas may be in equilibrium with respect to compression energy, because it can change freely the volume Vsys. Therefore, the pressure of the system psys is equal to the atmospheric pressure ... 

We can use Boyle s law to determine how the volume of a gas changes when its pressure changes. For example, if a cylinder fitted with a movable piston holds 50.0 L of O2 gas at 18.5 atm and 21 °C, what volume will the gas occupy if the temperature is maintained at 21 °C while the pressure is reduced to 1.00 atm Because the product PV is a constant when a gas is held at constant n and T, we know that... 

The pressure of a gas sample depends, in part, on its volume. If the temperature and the amount of gas are constant, tiie pressure of a gas sample increases for a decrease in volume and decreases for an increase in volume. A simple hand pump, for example, works on this principle. A hand pump is basically a cylinder equipped with a moveable piston (T Figure 11.11). The volume in the cylinder increases when you pull the handle up (the upstroke) and decreases when you push the handle down (the downstroke). On the upstroke, the increasing voliune causes a decrease in the internal pressure (the pressure within the pump s cylinder). This, in turn, draws air into the pump s cylinder through a one-way valve. On the downstroke, the decreasing volume causes an increase in the internal pressure. This increase forces the air out of the pump, through a different one-way valve, and into the tire or whatever else is being inflated. 

EXAMPLE 11.2 Boyle S Law A cylinder equipped with a moveable piston has an applied pressure of 4.0 atm and a volume of 6.0 L. What is the volume of the cylinder if the applied pressure is decreased to 1.0 atm ... 

When properties of a system change and the system moves from one thermodynamic equilibrium state to another, the path of succession of states that the system passes through is defined as the process. For example, the gas in a cylinder-piston arrangement shown in Figure 3.1 undergoes an expansion process from state 1 with pressure, Pj, and volume, W, to state 2 with pressure, 2, and volume, V2. 

How does a system in chemical equiUbrium respond to a volume change Recall from Chapter 5 that changing the volnme of a gas (or a gas mixture) results in a change in pressure. Remember also that pressure and volume are inversely related a decrease in volume causes an increase in pressure, and an increase in volume causes a decrease in pressure. So, if the volume of a reaction mixture at chemical equiUbrium is changed, the pressure changes and the system shifts in a direction to minimize that change. For example, consider the following reaction at equiUbrium in a cylinder equipped with a moveable piston ... 

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