A power cycle operating at steady state receives energy by heat transfer at a rate Q_H at T_H = 1800 K and rejects energy by heat transfer to a cold reservoir at a rate Q_C at T_C = 600 K. For each of the following cases, determine whether the cycle operates reversibly, operates irreversibly, or is impossible.
Q._H = 500 kW, Q._C = 100 kW
Q._H = 500 kW, W._cycle = 250 kW,
Q._C = 200 kW W_cycle = 350 kW,
Q._C = 150 kW Q._H = 500 kW, Q._C = 200 kW

Explaynation:

Operation between the two power cycle reserviors

Energy from cold reservoir QC

Energy from hot reservoir QH Temperature of cold reservoir TC

Temperature of hot reservoir TH

to know if the cycle if the first cycle operates reversibly, irreversibly or impossible

FIRST STEP

*FIND MAXIMUM COEFFICIENT OF PERFORMANCE FOR THE POWER CYCLE OPERATING BETWEEN THE TWO RESERVOIR

Cm= TC/TH-TC = 600/1800-1200=0.5

*SECONDLY FIND THE COEFFICIENT OF PERFORMANCE FOR ANY OF THE CYCLE

C = QC/Wcycle

(a) QH = 500kw, QC = 100kw

Wcycle = QH - QC = 500 - 100= 400kw

C = 100/400= 0.25

Cm=0.5 C = 0.25

Cm>C (the cycle is irreversibly)

(b) QH = 500kw, Wcycle = 250kw

Wcycle= QH - QC

QC = QH-Wcyle

QC = 500-250= 250kw

C=QC/Wcycle

C=250/250

C= 1

Cm = 0.5 C = 1

C>Cm (the cycle is impossible)

(c) QC = 200kw, Wcycle= 350

C= QC/Wcycle= 200/350=0.57

Cm = 0.5 C = 0.57

C>Cm (the cycle is impossible)

(d) QC = 150kw, QH = 500

Wcycle = QH - QC = 500 - 150 = 350

C = QC/ Wcycle = 150/350= 0.428

Cm=0.5 C = 0.428

Cm>C (the cycle is irreversibly)

The power cycle becomes reversibly if Cm=C, from what we have so far, only impossible and irreversibly