Adiabatic compression work equation

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 ... 

So far only reversible adiabatic compression of an ideal gas has been considered. For the irreversible adiabatic compression of an actual gas, the shaft work W required to compress the gas from state 1 to state 2 can be obtained from equation 6.7, which in this case becomes... 

Watson correlation for latent heat, 116 Wilson equation, 379-381 Work, 11-14, 23-26, 138 of adiabatic compression, 67-68, 235-238 ideal, 549-554... 

The negative sign means that work is done on the gas when Ti > Ti, that is, in an adiabatic compression. Equation (10.8) may be combined with equations (10.4) or (10.6), so as to eliminate Ti and T2 and obtain expressions for the work of expansion in terms of the volumes or pressures, respectively. 

In the treatment of adiabatic processes in the text, the heat capacity has been assumed to be independent of temperature. How could allowance be made for the variation of Cp with temperature in equation (10.6) (The gas may be assumed to be ideal in other respects.) Use this method to estimate the work done, in calories, and the final temperature in the reversible, adiabatic compression of 1 mole of oxygen from 10 liters to 1 liter, the initial temperature being 26 C. What would be the result if Cp were taken as having the constant (mean) value of 7 cal. deg. mole ... 

Equation B.14 is the work required for an ideal adiabatic (isentropic) compression. To account for inefficiencies in the compression process and the mechanical inefficiency, the isentropic compression efficiency is introduced ... 

Whereas reciprocating compressors are normally designed on the basis of adiabatic work (together with an isentropic efficiency), centrifugal compressors are usually designed on the basis of polytropic work. By analogy with Equation B.15, the work required for a poly tropic compression is given by ... 

Equation 6.89 gives the theoretical adiabatic work of compression from pressure P to pressure P2. 

Adiabatic processes. Ratio of the specific heats. If the gas is contained in st vessel, the walls of which are impermeable to heat or adiabatic so that no interchange of heat with the surroundings is possible, the energy of the gas diminishes by the amount of the work done against the external pressure. On the other hand, if the gas is compressed, its energy increases by the amount of the work done in the compression. In the first case there is a fall, in the second a rise in the temperature of the gas. The magnitude of the change in temperature may be calculated from equation (2) as follows ... 

We are now in a position to deduce the equation of state of a Prevost chamber, and to determine the change in the energy density of the radiation produced by an adiabatic change in volume. The work done in compressing the radiation by dV... 

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%. 

Duct Flow of Compressible Fluids Thermodynamics provides equations interrelating pressure changes, velocity, duct cross-sectional area, enthalpy, entropy, and specific volume within a flowing stream. Considered ere is the adiabatic, steady-state, one-dimensional flow of a compressible fluid in the absence of shaft work and changes in potential energy. The appropriate energy balance is Eq. (4-155). With Q, Wj, and Az all set equal to zero,... 

As k —> 1), this expression reduces to Equation (5.148). For a given compression ratio, the isothermal work is always less than the isentropic work. However, most compressors operate under more nearly adiabatic conditions because of the relatively short residence time of the gas in the compressor. The temperature rise during an isentropic compression is... 

If you have ever pumped air into a bicycle tire, you probably noticed a warming effect at the valve stem. This phenomenon, too, can be explained by the first law of thermodynamics. The action of the pump compresses the air inside the pump and the tire. The process is rapid enough to be treated as approximately adiabatic, so that q = 0 and AE = w. Because work is done on the gas in this case (it is being compressed), w is positive, and there is an increase in energy. Hence, the temperature of the system increases also, according to the equation... 

This equation applies to both incompressible and compressible flow, and no condition of reversibility is implied. Row through a turbine nozzle is adiabatic, so that dq = 0 no work is done (until it reaches the turbine blade downstream of the nozzle), so that dw = 0 and the height difference is zero, so that dz = 0. Accordingly equation (4.7) simplifies to... 

The specific work required will be a minimum when the temperature, T2, is a minimum, and this will occur when the compression process is not only adiabatic but also reversible, that is isentropic. An isentropic compression is governed by the equation ... 

In Chapter 2, we learned that expansion work has the form dw = —p dl/. Can these expressions be reconciled, and if so, under what conditions First, note that the expression that multiplies dV in equation (a) refers to the sample, so if it is some sort of pressure, it must be the sample pressure, and not an arbitrary external pressure, so if the expressions can be reconciled, it must be for reversible adiabatic expansion or compression. The expression that multiplies dV can be expressed as... 

Problem 5.12 Oxygen is compressed by reversible adiabatic process in a closed system, from 1 bar, 20 °C to 10 bar. Assuming oxygen to follow the SRK equation of state, calculate the amount of required work. Hint Tabulate the entropy of oxygen at 10 bar at various temperatures and locate the temperature where the entropy is equal to that at 1 bar, 20 °C. 

Compression or Expansion. When gases or vapors are expanded or compressed under adiabatic conditions, the amount of work done and the amount of heat required are dependent upon the ratio of the specific heat at constant pressure to the specific heat at constant volume. The expansion of a gas can always be expressed by an equation of the form... 

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