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Linde - Hampson System oF Liquefaction Of Air

 In  this system, Joule -Kelvin effect is utilized for cooling, and ultimately , liquefying the air. Ideally the compression would be isothermal. A two-stage compressor with intercooling and aftercooling. The yield Y of  the system is defined as the ratio of mass of the liquid produced to the mass of gas compressed. The energy required per unit mass of  liquid produced is known as the specific work consumption, W. 



The theoretical yield, assuming perfect insulation, can be determined by a mass and energy balance for the control volume (Joule-Kelvin refrigeration system). Let m*,1 be the rate at which liquid air is produced 9 The same given to the system as make-up), and m* the rate at which air is compressed and then expanded. Then yield is 

Y = m*f / m*

 and the energy balance gives,

 m*h2 - m*f h5 - (m* -m*f ) h7 = 0

 m*(h2-h1) -m*f(h5-h7)  = 0

 Y = m*f  / m* = (h2-h7) / (h5-h7) 

  Y= (h7 - h2) / (h7 - h5)

  No yield is thus possible unless h7 is greater than h2. The energy balance for the compressor gives 

m*h1 + Wc = m*h2 + Qr

Where Qr is the heat loss to the surroundings from the compressor 

Wc / m*  =  T1 (S1-S2) - (h1-h2)

This is the minimum work requirement. 

Specific work consumption, W  =Wc m* /  m* m*f 

                                               W = Wc / m*Y 


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