Gases piston-cylinder arrangement

To indicate the nature of reversible processes, we examine the simple expansion of a gas in a piston/cylinder arrangement. The apparatus is shown in Fig. 2.4, and is imagined to exist in an evacuated space. The gas trapped inside the cylinder is chosen as the system all else is the surroundings. Expansion processes result when mass is removed from the piston. To make the process as simple as possible, we assume that the piston slides within the cylinder without friction and that the piston and cylinder neither absorb nor transmit heat. Moreover, because the density of the gas in the cylinder is low and because the mass of gas is small, we ignore the effects of gravity on the contents of the... 

COMPRESSION/EXPANSION OF AN IDEAL GAS Consider an ideal gas enclosed in a piston-cylinder arrangement that is maintained at constant temperature in a heat bath. The gas can be compressed (or expanded) reversibly by changing the position of the piston to accomplish a specified change in volume. In Section 12.6, the heat transferred between system and bath when the gas is expanded (or compressed) isothermally and reversibly from volume Vi to Vi is shown to be... 

IRREVERSIBLE EXPANSION OF AN IDEAL GAS Consider a gas confined within a piston-cylinder arrangement and held at constant temperature in a heat bath. Suppose the external pressure is abruptly reduced and held constant at the new lower value. The gas immediately expands against the piston until its internal pressure declines to match the new external pressure. The total entropy of system plus surroundings will increase during this expansion. In preparation for a quantitative example, a general comparison of irreversible and reversible processes connecting the same initial and final states provides insight into why the total entropy increases in a spontaneous process. 

Consider a thermostatted piston-cylinder arrangement as shown in Figure 4.6. The cylinder is fitted with a number of devices which can hold the piston in position at various levels. When the piston is held stationary, the pressure of the gas, Pinu is of course exactly balanced by the pressure exerted by the stop devices. Perhaps more exactly, the force exerted by the stops plus the force exerted by the piston mass divided by the area of the piston gives a pressure P,>xt) equal and opposite to the gas pressure when the piston is held still. If the stops are removed, then all of a sudden... 

The mixture will start condensing once the dew pressure hits the value of the applied pressure, that is, P = 760 mm Hg. That means above the dew-point temperature, which is to be found, the gas mixture is considered to be superheated. At the dew-point temperature, the first liquid droplet starts to form, hence the name dew-point temperature. As we have a mixture of two substances having different condensing point temperatures, then the dew-point temperature for the rest of the vapor mixture (which is now richer in benzene and poorer in toluene) will be lower than that at which we calculate the formation of the first droplet. That simply means we have to decrease the temperature to continue the process of condensation. Because we initially have a gas phase, the cooling process will be carried out in a closed system under constant pressure piston-cylinder arrangement in which the total volume will decrease as a result of cooling until all vapor condenses and we reach a liquid mixture with same initial vapor composition but at its bubble-point temperature. 

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. 

Example 2.11 The piston-and-cylinder arrangement shown in Fig. 2.6 contains nitrogen gas trapped below the piston at a pressure of 7 bar. The piston is held in... 

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. 

As a model for the work involved in changing the volume of a gas, consider the arrangement shown in Fig. 3.4 on the next page. A sample of gas is confined in a cylinder by a piston. The system is the gas. The piston is not part of the system, but its position given by the variable x determines the system s volume. Movement of the piston to the right, in the -l-x direction, expands the gas movement to the left, in the —x direction, compresses it. 

The P-Vdata of Table 2.E.1 were obtained using steam in a piston-and-cylinder arrangement, placed in a large bath of constant hotness. What is the corresponding ideal gas temperature of the bath ... 

The so-called hypercompressors for the production of LDPE represent a special case. The ethylene is compressed in a primary piston compressor, with several stages up to around 200 to 300 bar the hypercompressor (or secondary compressor) brings the gas up from there to 3000 bar. The hypercompressors show pairwise-opposite-cylinders, and are built with up to fourteen cylinders in a multiplex arrangement. The components loaded by an internally pulsating pressure are either shrunk and/or autofrettage-treated in order to implement protective compressive residual stresses (Fig. 4.1-34). 

Consider the cylinder filled with air and with the piston and spring arrangement shown below. The external atmospheric pressure is 1 bar, the initial temperature of the air is 25 C, the no-load length of the spring is 50 cm, the spring constant is 40 000 N/m, the frictionless piston weighs 500 kg, and the constant-volume heat capacity of air can be taken to be constant at 20.3 J/(mol K). Assume air is an ideal gas. Compute... 

Now let s consider another example, the expansion of an ideal gas at constant temperature (referred to as an isothermal process). In the cylinder-piston arrangement of Figure 19.5, when the partition is removed, the gas expands spontaneously to fill the evacuated space. Can we determine whether this particular isothermal expansion is reversible or irreversible Because the gas expands into a vacuum with no external... 

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. 

Consider a large bath - large enough that its hotness is not effected by the transfer to, or from it, of a small amount of energy - in which we place a cylinder-and-piston arrangement containing one mole of nitrogen. After thermal equilibrium is reached, we record the pressure (Pj) and volume (Vj) of the gas inside the cylinder. 

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