Adiabatic piston

A closed system cannot perforin an isentropic process without performing work. Example (Fig. 3) A quantity of gas enclosed by an ideal, tfictionless, adiabatic piston in an adiabatic cylinder is maintained at a pressure p by a suitable ideal mechanism, so that Gl = pA (A being the area of piston). When the weight G is increased (or decreased) by an infinitesimal amount dG, the gas will undergo an isentropic compression (or expansion). In this case,... 

One kilogram of saturated liquid methane at 160 K is placed in an adiabatic piston-and-cylinder device, and the piston will be moved slowly and reversibly until 25 percent of the liquid has vaporized. Compute the maximum work that can be obtained, assuming that methane is described by the Peng-Robinson equation of state. Compare your results with the solution to Problem 4.39. 

TABLE 3.1 Summary of Entropy Change for Reversible and Irreversible Expansion (or Compression) of the Adiabatic Piston-Cylinder Assembly in Case I... 

Consider two ideal-gas subsystems a and (3 coupled by a movable diatliemiic wall (piston) as shown in figure A2.1.5. The wall is held in place at a fixed position / by a stop (pin) that can be removed then the wall is free to move to a new position / . The total system (a -t P) is adiabatically enclosed, indeed isolated q = w = 0), so the total energy, volume and number of moles are fixed. 

For an ideal gas and a diathemiic piston, the condition of constant energy means constant temperature. The reverse change can then be carried out simply by relaxing the adiabatic constraint on the external walls and innnersing the system in a themiostatic bath. More generally tlie initial state and the final state may be at different temperatures so that one may have to have a series of temperature baths to ensure that the entire series of steps is reversible. 

Triaryl phosphates of ISO 32 viscosity show promise for the main beating lubricants of steam and gas turbiaes (39,40). An interesting possibiHty iavolves unique deHvery of phosphate ester vapor to lubricate the piston ring 2one of low heat rejection (adiabatic) diesel engines (41). 

It follows that the efficiency of the Carnot engine is entirely determined by the temperatures of the two isothermal processes. The Otto cycle, being a real process, does not have ideal isothermal or adiabatic expansion and contraction of the gas phase due to the finite thermal losses of the combustion chamber and resistance to the movement of the piston, and because the product gases are not at tlrermodynamic equilibrium. Furthermore the heat of combustion is mainly evolved during a short time, after the gas has been compressed by the piston. This gives rise to an additional increase in temperature which is not accompanied by a large change in volume due to the constraint applied by tire piston. The efficiency, QE, expressed as a function of the compression ratio (r) can only be assumed therefore to be an approximation to the ideal gas Carnot cycle. 

A reversible adiabatic process is known as isentropic. Thus, the two conditions are directly related. In actual practice compressors generate friction heat, give off heat, have valve leakage and have piston ring leakage. These deviations... 

Horsepower is the work done in a cylinder on the gas by the piston connected to the driver during the complete compression cycle. The theoretical horsepower is that required to isen-tropically (adiabatically) compress a gas through a specified pressure range. The indicated horsepower is the actual work of compression developed in the compressor cylinder(s) as determined from an indicator card. Brake horsepower (bhp) is the actual horsepower input at the crankshaft of the compressor drive. It does not include the losses in the driver itself, but is rather the actual net horsepower that the driver must deliver to the compressor crankshaft. 

Cg,. = compression efficiency, the product of adiabatic and reversible efficiencies, which vary with the cylinder and valve design, piston speed, and fraction values range from 0.70-0.88 usually. 

The process occurring when steam is expanded by conversion to work without external heat loss or gain. Steam expanding behind the piston of a steam engine after the cutoff point approaches adiabatic expansion. 

The results in Table 6.3 show that isothermal piston flow is not always the best environment for consecutive reactions. The adiabatic temperature profile gives better results, and there is no reason to suppose that it is the best... 

Correlations for E are not widely available. The more accurate model given in Section 9.1 is preferred for nonisothermal reactions in packed-beds. However, as discussed previously, this model degenerates to piston flow for an adiabatic reaction. The nonisothermal axial dispersion model is a conservative design methodology available for adiabatic reactions in packed beds and for nonisothermal reactions in turbulent pipeline flows. The fact that E >D provides some basis for estimating E. Recognize that the axial dispersion model is a correction to what would otherwise be treated as piston flow. Thus, even setting E=D should improve the accuracy of the predictions. 

Figure 2. The adiabatic pistion separates compartments to its left and right filled with gases at temperature T and T2 and pressure Pi and P2, respectively. Does the piston move when Pi = P2 but Ti + T2 ...

It can be stabilized against explosion by shock (adiabatic compression by a piston) by adding 75 parts by weight of either EtOH,... 

Figure 3.9 Schematic representation of (a) an adiabatic container, allowing PV work by movement of a piston, but unaffected by other changes in the surroundings (b) a diathermal (nonadiabatic) container, allowing thermal equilibration with the surroundings.

Unfortunately, valve disablers have a detrimental effect on the adiabatic compressor efficiency. This means that, even though no gas may be moving through the crank end of a cylinder, the piston is still doing work on the gas inside the crank end of the cylinder. If you would like proof, place your hand on the valve cap on such a disabled cylinder. The high temperature you will feel is wasted compression work going to useless heat. I have measured in the field that, after a cylinder end is completely disabled, it is still converting 20 percent of the former compression work to heat. 

In an idealized Joule-Thomson experiment (also called the Joule-Kelvin experiment) a gas is confined by pistons in a cylinder that is divided into two parts by, a rigid porous membrane (see Fig. 7.3). The gas, starting at pressure P, and temperature 7, is expanded adiabatically and quasi-statically through the membrane to pressure P2 and temperature T2. The two pressures are kept constant during the experiment. If V1 is the initial volume of the number of moles of gas that pass through the membrane and V2 is the final volume of this quantity of gas, then the work done by the gas... 

The best-known model for FCC risers may be that of Paraskos et al. (8) and Shah et al. (8), although their valuable work is already a little old (published in 1976-1977). They considered the riser to be isothermal (7) and adiabatic (8). Besides piston flow in the riser, they assumed a deactivation order (d) of 1, which is, for us, an important error, and a slip velocity of unity (in reality they only mention one time, their rj). 

Suppose a gas in a piston expands slowly from pressure P and volume V to pressure Pi and volume Vi, in the process doing work against the atmosphere. In many cases we can assume the expansion is adiabatic, meaning that no heat enters the gas during the expansion. If the heat capacity is independent of temperature, it can be shown that P = Pi V/, where the ratio y = cp/cv is the same quantity encountered in the speed-of-sound expression, Equation 7.29. 

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