Compression work

Wlien a spring is stretched or compressed, work is done. If the spring is the system, then the work done on it is simply... 

The theoretical required (isothermal) compression work in the compressor, which is assumed to operate isothermally at To, is... 

Voile, M., Brisson, M., Perusse, M., Tanaka, M., Doyon, Y. (1979). Compressed Work Week Psychophysiological and Physiological Repercussions. Ergonomics 22, 1011-1010. 

Figure 12-70. Entropy-temperature diagrams help to solve compression work problems. Data for ammonia provided. (Used by permission Corrigan, T. E. and A. F. Johnson. Chemical Engineering, V. 61, No. 1, 1954. McGraw-Hill, Inc. All rights reserved.)...

Consider a volume of gas flowing into the compressor. Compression work W, is required to force the gas into the system. The constant force exerted on the gas is P At, where A is the cross-sectional area of the inlet duct. The distance through which the gas is forced as it enters the system is - V / A. The negative value of - V /A results from the force acting from the surroundings on the system. Thus ... 

The compression work cannot be evaluated from Eq. (8-15) using Eq. (8-17) unless the operating condition or temperature is specified. We will consider two cases isothermal compression and adiabatic compression. 

In reality, most compressor conditions are neither purely isothermal nor purely isentropic but somewhere in between. This can be accounted for in calculating the compression work by using the isentropic equation [Eq. (8-21)], but replacing the specific heat ratio k by a polytropic constant, y, where 1 < y < k. The value of y is a function of the compressor design as well as the properties of the gas. 

When 3He is compressed, a mechanical work pdV is done. The ratio between the compression work and the cooling power is shown in Fig. 7.4. If some irreversible process takes place during the compression, the heating may exceed the cooling. In practice, this happens at 0.7-0.8mK. 

The effect of temperature on the equation of state is introduced through the iso-baric thermal expansivity. It is generally assumed that isobaric expansivity and iso-baric compressibility work independently of each order and the volume as a function of T and p is then expressed as... 

In the case of compression from pressure P to pressure P2 through n stages each having the same pressure ratio (P2/Pi)Vn, the compression work is given by... 

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. 

An engine operates on an Otto cycle with a compression ratio of 8. At the beginning of the isentropic compression process, the volume, pressure, and temperature of the air are 0.01 m, llOkPa, and 50°C. At the end of the combustion process, the temperature is 900°C. Find (a) the temperature at the remaining two states of the Otto cycle, (b) the pressure of the gas at the end of the combustion process, (c) the heat added per unit mass to the engine in the combustion chamber, (d) the heat removed per unit mass from the engine to the environment, (e) the compression work per unit mass added, (f) the expansion work per unit mass done, (g) MEP, and (h) thermal cycle efficiency. 

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 compression work depends on the nature of the gas (Table 5.2). Real compressors work close to the isothermal limit (Figure 5.3). 

Figure 5.3 Work for isothermal (solid line) and adiabatic (dotted line) compression of hydrogen from an initial pressure ofpj = 1 bar on the left axis. Compression work as a percentage of the higher heating value (39.4 kWh l ) of hydrogen on the right axis.

This chapter establishes the basis for the Second Law of Thermodynamics. It is not critical that you read this chapter to be able to understand the more practical chapters on compression that follow. But, for those readers who have technical training, wouldn t it be lovely to actually understand the basis for the Second Law of Thermodynamics. Wouldn t it be grand to really see the beauty and simplicity of the basis for the adiabatic compression work equation ... 

The specific heat at constant volume (i.e., CL.) is a measure of the amount of heat we put into the air, trapped inside the cylinder. All this heat goes to increasing the temperature of the trapped air by 1°F. None of the heat goes into compression work, because the piston remains fixed. 

How can we determine how much work is being done There are two ways to calculate the amount of compression work that the piston is doing on the atmosphere of air surrounding the planet ... 

Does that look familiar It really ought to, if you have any type of engineering training. Remember the formula for compression work, given at the start of this chapter, and in our thermodynamics textbooks ... 

This simplified version assumes that K (the Cp/Cv ratio) is a constant of 1.3 that Tv the suction temperature, is constant and that the compression work is proportional to the motor amps (N is the number of moles of gas flowing into the compressor). From Eq. (28.2), it is obvious... 

Caution The equations presented in this chapter for polytropic head and compression work have been simplified for clarity. They cannot be used for rigorous engineering calculations.)... 

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. 

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