Irreversible processes isothermal compression

The Linde>Hampson process uses a thermodynamic process. Isothermal compression and subsequent cooling along an isobar is done in a heat exchanger. Joule-Thomson expansion connected with an irreversible change in entropy is used as the refrigeration procedure. Despite its simplicity and reliability, this method is now less attractive compared with new ones where cooling is primarily carried out in reversible processes (expander) and where less energy is required. 

One mole of a monatomic ideal gas begins in a state with P = 1.00 atm and T = 300 K. It is expanded reversibly and adiabatically until the volume has doubled then it is expanded irreversibly and isothermally into a vacuum until the volume has doubled again and then it is heated reversibly at constant volnme to 400 K. Finally, it is compressed reversibly and isothermally until a final state with P = 1.00 atm and T = 400 K is reached. Calculate AS for this process. Hint There are two ways to solve this problem—an easy way and a hard way.)... 

In order to calculate the entropy changes in the two reservoirs after this irreversible process has occurred, we must devise a way of transferring the heat reversibly, since an entropy change can be calculated directly only for a reversible process. We can make use of an ideal gas to carry out the heat transfer process, as shown in Figure 5.56. The gas is contained in a cylinder with a piston. We first place it in the warm reservoir, at temperature Ti, and expand it reversibly and isothermally until it has taken up heat equal to q. The gas is then removed from the hot reservoir, placed in an insulated container, and allowed to expand reversibly and adiabatically until its temperature has fallen to T. Finally, the gas is placed in contact with the colder reservoir at Tc and compressed isothermally until it has given up heat equal to q. 

Lets review the mechanical process from which we learned about reversibOity and irreversibOity. In Section 2.3, we considered a piston-cylinder assembly that underwent an isothermal expansion/compression, as shown in Figure 3.2u. When we remove the 1020-kg block, as depicted on the left, the piston expands irreversibly. Likewise, when we replace the block on the piston, it compresses irreversibly. In this case, the driving force for change is a pressure difference. The processes are illustrated on the Pv curve at the bottom. Notice that the irreversible processes have a definite directionality. The arrows that describe the expansion process do not overlap with those that describe the compression process. As we saw, the work needed to compress the assembly was greater than the work obtained from expanding it and is represented by a very different directional process (with different arrows and different shaded area on the Pv curve). The irreversible expansion and compression processes are distinct and different. 

EXAMPLES. Calculation of Entropy Change for an Irreversible, Isothermal Compression A piston-cylinder device initially contains 0.50 of an ideal gas at 150 kPa and 20°C. The gas is subjected to a constant external pressure of 400 kPa and compressed in an isothermal process. Assume the surroundings are at 20 C. Take Cp = 25R and assume the ideal gas model holds. (a) Determine the heat transfer (in kj) during the process. (b) What is the entropy change of the system, surroundings, and universe (c) Is the process reversible, irreversible, or impossible ... 

Herein, we expand on the discussion of our recently observed isothermal amorphous-amorphous-amorphous transition sequence. We achieved to compress LDA in an isothermal, dilatometric experiment at 125 K in a stepwise fashion via HDA to VHDA. However, we can not distinguish if this stepwise process is a kinetically controlled continuous process or if both steps are true phase transitions (of first or higher order). We want to emphasize that the main focus here is to investigate transitions between different amorphous states at elevated pressures rather than the annealing effects observed at 1 bar. The vast majority of computational studies shows qualitatively similar features in the metastable phase diagram of amorphous water (cf. e.g. Fig.l in ref. 39) at elevated pressures the thermodynamic equilibrium line between HDA and LDA can be reversibly crossed, whereas by heating at 1 bar the spinodal is irreversibly crossed. These two fundamentally different mechanisms need to be scrutinized separately. 

Figure 3.2 Illustration of irreversible and reversible processes, (a) Mechanical process of isothermal expansion/compression. (b) Thermal process in which work can be obtained from a Carnot engine.

To illustrate how entropy tells us about the directionahty of nature, we first pick a set of four mechanical processes similar to those described in Figure 3.2a (1) reversible expansion, (2) irreversible expansion, (3) reversible compression, and (4) irreversible compression. In this case, however, we choose adiabatic rather than isothermal processes. The adiabatic process represents the limit of no heat transfer between the system and the... 

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