5.49 Shown in Fig. P5.49 is a system consisting of a power cycle and a heat pump

Question

5.49 Shown in Fig. P5.49 is a system consisting of a power cycle and a heat pump cycle, each operating between hot and cold reservoirs whose temperature are 500 K and 300 K, respectively. All energy transfers are positive in the 5 directions of the arrows. The accompanying table provides two sets of steady-state data, in kW. For each set of data, determine if the system is operating in accord with the first and second laws of thermodynamics Power cycle Heat pump cycde (a) 60 40 8060 0 (b) 12040100 100 80 20 Hot reservoir, TH 500 K Heat pump Power cycle 2c Fig.P5.49

Explanation / Answer

I alw of thermodynamics

Qh = Qc + W

power cycle

efficiency = n1 = Th/Th - Tc = 500/(500-300) = 5/2 = 2.5

(a)

Qh = 40 + 20 = 60

efficiency = Qh/Qh-Qc = 60/(60-40) = 3 not equa to 2.5

secod law is not obeyed

(b)

Qh = 80 + 40 = 120

efficiency = Qh/W = 120/40 = 3 not equa to 2.5

secod law is not obeyed

heat pump

efficiency n2 = Tc/(Th-Tc) = 300/(500-300) = 1.5

(a)

Qh = Qc + W = 60 + 20 = 80

efficiency = Qc/(Qh-Qc) = 60/(80-20) = 60/40 = 3/2 = 1.5 same as n2

secod law is obeyed

(b)

Qh = 80 + 20 = 100

efficiency = 80/(100-20) = 80/80 = 1 not equal to n2

secod law is not obeyed

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