In a simple Linde gas-liquefaction plant (see Fig. 18.13), air is taken in at the ambient conditions of 1 bar and \(300 \mathrm{~K}\). The water-jacketed compressor delivers the air at 200 bar and \(300 \mathrm{~K}\) and has an isothermal efficiency of \(70 \%\). There is zero temperature difference at the warm end of the regenerative heat exchanger (i.e. \(T_{2}=T_{7}\) ). Saturated liquid air is delivered at a pressure of 1 bar. Heat leakages into the plant and pressure drops in the heat exchanger and piping can be neglected.

Calculate the yield of liquid air per unit mass of air compressed, the work input per kilogram of air liquefied, and the rational efficiency of the liquefaction process.

[7.76\%; 8.39 MJ/kg; 8.84\%].

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(a) Compressor Electric motor m=1 Throttle Receiver 5 Make-up gas QA System boundary Liquid yield 6 m=1-y Temperature, T (b) 290 K 5 200 bar m=1 Isenthalpic line 6 Interstage cooling 1 bar m = (1-y) QA Entropy, S FIGURE 18.13 Simplified Linde gas-liquefaction plant. (a) Schematic diagram of simplified plant; (b) T-s diagram for liquefaction process.