THEORY Thermodynamically, the heat pump can be described as a heat-engine in which the following processes take place (Figure 4.5):

(i) Overheads from the column is compressed, path A3 on Figure 4.9.

(ii) The compressed overheads is cooled and condensed at the column rebciler, path BC on Figure 4.9.

(iii) The condensed overheads is expanded across the reflux control valve, path CD on Figure 4.9.

(iv) The liquid is boiled and converted into vapor by the column action, path DA on Figure 4.9.

Work is done during process (i). Processes (ii) and (iv) above are essentially isothermal. If Q is the reboil heat in process (ii) , and Q is the heat absorbed in process (iv), then the first law of thermSdvnamics gives

The second law of thermodynamics gives

Combining the above equations, one gets

T is simply the column overhead temperature. T is the condensation timperature at the reboiler, and can be expressed in terms of the column bottom temperature T and an approach AT, ie

The above is valid for an ideal cycle; for a non-ideal cycle a combined compressor efficiency term is added so that

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