Ideal compression work

Professor Nicolas L. S. Carnot, in the late nineteenth century, realized that the area inside the plot of pressure vs. volume represented the work needed to compress gas in a reciprocating compressor. In other words, the change of pressure, multiplied by the change in volume, is equal to the work done by the piston on the gas. Professor Carnot called this PV (pressure vs. volume) work. He then used calculus to sum up the area inside the lines shown in Fig. 29.2. The total area is now called ideal compression work. 

The Carnot cycle plot represents ideal compression work. But we in the process industry have to worry about actual compression work, and the loss of compression efficiency caused by these three problems. 

The solid line is the indicator-card plot. The dotted line is the Carnot or ideal compression work cycle which I have drawn myself. The piston position, shown on the horizontal axis, is proportional to the volume of gas inside the cylinder. 

In computer simulation the (ideal) compression work in adiabatic operation is calculated usually as the variation in enthalpy of the gas mixture between initial state, 7j and final state P2, T2 (see also eq. 5.20) ... 

Ideal compression work Compression work discoimting friction, leakage, and other mechanical losses. 

Carnot called this PV (pressure vs. volume) work. He then used calculus to sum up the area inside the lines shown in Fig. 36.2. The total area is now called ideal compression work. 

In this example we describe the calculation of the minimum work for ideal compressible adiabatic flow using two different optimization techniques, (a) analytical, and (b) numerical. Most real flows lie somewhere between adiabatic and isothermal flow. For adiabatic flow, the case examined here, you cannot establish a priori the relationship between pressure and density of the gas because the temperature is unknown as a function of pressure or density, hence the relation between pressure and... 

Energy is needed to eompress gases. The compression work depends on the thermodynamic compression process. The ideal isothermal compression cannot be realized. Even more energy is needed to compact hydrogen by liquefaction. Low density and extremely low boiling point of hydrogen increases the energy cost of compression or hquefaction. 

Determine the temperature at the end of the compression process, compression work, expansion work, and thermal efficiency of an ideal Otto cycle. The volumes of the cylinder before and after compression are 3 liters and 0.3 liter. Heat added to the air in the combustion chamber is 800kJ/kg. What is the mass of air in the cylinder The atmosphere conditions are 101.3 kPa and 20°C. 

Compression of hydrogen consumes energy depending on the thermodynamic process. The ideal isothermal compression requires the least amount of energy (just compression work) and the adiabatic process requires the maximum amount of energy. The compression energy W depends on the initial pressure p and the final pressure pf, the initial volume V and the adiabatic coefficient y ... 

The area enclosed by the solid line is the total or actual compression work. The area enclosed by the dotted line is ideal or useful compression work. The areas between the dotted line and the solid line represent compression work lost to heat. The area inside the dotted line, divided by the area inside the solid line, is called adiabatic compressor efficiency. 

In an ideal rocket, the combustionand expansion steps are the same as those for an ideal jet engine (Fig. 8.12). A solid-fuel rocket requires no compression work, and in a liquid-fuel rocket the compressionenergy is small, since the fuel and oxidizer are pumped as hquids. 

It will be recalled from the statements in 9d that in an isothermal, reversible expansion of an ideal gas the work done is exactly equal to the heat absorbed by the system. In other words, in this process the heat is completely converted into work. However, it is important to observe that this conversion is accompanied by an increase in the volume of the gas, so that the system has undergone a change. If the gas is to be restored to its original volume by reversible compression, work will have to be done on the system, and an equivalent amount of heat will be liberated. The work and heat quantities involved in the process are exactly the same as those concerned in the original expansion. Hence, the net result of the isothermal expansion and compression is that the system is restored to its original state, but there is no net absorption of heat and no work is done. The foregoing is an illustration of the universal experience, that it is not possible to convert... 

The ideal compression (in isothermal conditions) work can be calculated according to the following equation ... 

The ideal, adiabatic work compression can then be calculated from the difference in the enthalpies ... 

The reversible pulse tube refrigerator does not utilize a flow-reversing valve but raises and lowers the pressure in the system by means of a reversible piston. If all of the components of the system are assumed to be ideal, the work of compression would be about equal to the work of expansion. As the... 

In simplifying the expansion-compression work term in Eq. (114), use has been made of overall continuity and the fact that for an ideal gas, Spl(>T)ii = PIT. 

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