Compression reversible work

The working substance being initially at the temperature T2 of the refrigerator, we place the cylinder on the non-conducting stand, and compress the working substance reversibly until the temperature rises to Ti. By the conditions imposed, this is an adiabatic compression, and will be represented by a continuous curve on the indicator diagram, say AB (Fig. 8). 

Finally, the cylinder is placed on the refrigerator and the working substance compressed reversibly and isothermally until it returns to its initial state A, rejecting heat Q2 to the refrigerator. This operation is represented by the curve DA. 

A hypothetical cycle for achieving reversible work, typically consisting of a sequence of operations (1) isothermal expansion of an ideal gas at a temperature T2 (2) adiabatic expansion from T2 to Ti (3) isothermal compression at temperature Ti and (4) adiabatic compression from Ti to T2. This cycle represents the action of an ideal heat engine, one exhibiting maximum thermal efficiency. Inferences drawn from thermodynamic consideration of Carnot cycles have advanced our understanding about the thermodynamics of chemical systems. See Carnot s Theorem Efficiency Thermodynamics... 

Finally, we compress the fluid adiabatically and reversibly from D to A, thus completing the cycle. In this compression the work, WA, is done by the surroundings on the fluid (a positive quantity) and no heat is transferred from or to the system. 

Calculate the reversible work of compression on 100 g of a liquid when the pressure is increased from 10 to 100 atm at a constant temperature of 20°C. The compressibility is jJ - 82 x 10"6 atm"1. Assume that / is constant within the pressure range 1 to 100 atm, and that the density of the liquid, p, at 20°C and 1 atm pressure is 0.792 g/cm3. What assumptions have you introduced carrying out these particular calculations ... 

As the gas is compressed reversibly and isothermally, it releases 1.4PiVi (L atm) of energy as heat to the surroundings. In other words, the same quantity of energy flows into the gas as work and flows out of the gas as heat to produce no net change in E as the compression occurs. 

Calculate the work done on an ideal gas when it is compressed reversibly (Section 12.2, Problems 1-2). 

Suppose 2.00 mol of an ideal gas is contained in a heat-insulated cylinder with a moveable frictionless piston. Initially, the gas is at 1.00 atm and 0°C. The gas is compressed reversibly to 2.00 atm. The molar heat capacity at constant pressure, Cp, equals 29.3 J mol . Calculate the final temperature of the gas, the change in its internal energy, AU, and the work done on the gas. 

Calculate the reversible work required to compress 5 of an ideal gas initially at 100°F from 1 to 10 atm in an adiabatic cylinder. Such a gas has an equation of state pV - == constant. Then calculate the actual work required if the efficiency of the process is 80%. 

Fig. 12. Calculation of the time correlation function C t) is equivalent to determining the reversible work Wab it) required to confine the endpoints of paths originating from region A into region B. This amounts to a compression of pathways in trajectory space...

Determine the reversible work, in liter-atm., required to expand 1 mole of carbon dioxide isothermally from an initial pressure of 200 atm. to a final pressure of 1 atm. at 50 C, assuming van der Waals behavior. (Instead of solving the cubic equation to obtain the initial and final volumes, they may be obtained more simply by means of the generalized compressibility diagram.) Compare the result mib, that to be expect for an ideal gas. 

Furthermore, a real machine designed for adiabatic compression does not reach the ideal point of reversible iso-entropic process, because of unavoidable irreversible transformations. The reversible work associated to the pressure increase inside a fluid can be always calculated as vdp, while the net enthalpy variation is directly related to mechanical energy consumption, which increases with irreversibilities. 

Third Step —The system, now at the lower temperature, is lsother-mally and reversibly compressed, the work done upon it being represented by the area below CI>, viz QPiHK It gives out a quantity of heat at this lower temperature, which is a little less than Q... 

Ethylene is compressed reversibly in a closed system. The compression is conducted isothermally at 350 K, from initial pressure 20 bar to final pressure 55 bar. Calculate the work using the SRK equation of state. 

This is a special process in which the system exchanges reversible work with the surroundings but no heat. Experimentally, this can be accomplished by thermally insulating the system and conducting the process in a quasi-static manner. Such system can either be compressed or expanded. The conditions reversible and adiabatic fully specify the path, as we will see below. The process is not specific to ideal-gases, but the calculation of this path for a general fluid will be delayed until Chapter d. 

The second term on the right-hand side of Eq. 1 represents the reversible work done by the fluid against the external pressure field this term is linked to the compressibility of the fluid and is known in the literature as flow work. The third term on the right-hand side of Eq. 1 is linked to the work done by the fluid on adjacent layers due to the action of the shear forces this work is transformed into heat by means of an irreversible process called viscous dissipation in the English language literature and as internal friction in the Russian literature. 

The third term indicates the work associated with the expansion and compression of the fluid (a reversible work). 

The situation is different when the piston moves at an appreciable finite rate. The frictional work Wfric is then positive. As a result, the irreversible work of expansion is less negative than the reversible work for the same volume increase, and the irreversible work of compression is more positive than the reversible work for the same volume decrease. These effects of piston velocity on the work are consistent with the minimal work principle. 

If the process of water vapor compression is described like that for an ideal gas undergoing an adiabatic process, then the reversible work required for the compression is given by that for an isentropic process ... 

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