**(a) The cycle is not possible.**

**(b) The cycle operates irreversibly.**

**(c) The cycle operates irreversibly.**

**(d) The cycle is not possible.**

<u>**Explanation:**</u>

Given -

Temperature of hot reservoir, Th = 1500K

Temperature of cold reservoir, Tc = 500K

(a)

Heat transfer at hot reservoir, Qh = 550 kW

Heat transfer at cold reservoir, Qc = 100 kW

Maximum net work -

Wcycle = Qh - Qc

Wcycle = 550 - 100 = 450kW

Maximum efficiency -

ηmax = 1 - Tc/Th

ηmax = 1 - 500/1500 = 0.667

ηmax = 66.7%

η(actual) = Wcycle/ Qh

η(actual) = 450 kW/ 550 = 0.8

η(actual) = 80%

**Since the actual efficiency is higher than the maximum efficiency, the cycle is not possible.**

(b)

Heat transfer at hot reservoir, Qh = 500 kW

Heat transfer at cold reservoir, Qc = 200 kW

Maximum net work -

Wcycle = Qh - Qc

Wcycle = 500 - 200 = 300kW

Maximum efficiency -

ηmax = 1 - Tc/Th

ηmax = 1 - 500/1500 = 0.667

ηmax = 66.7%

η(actual) = Wcycle/ Qh

η(actual) = 300 kW/ 500 = 0.6

η(actual) = 60%

**Since the actual efficiency is lower than the maximum efficiency, the cycle operates irreversibly.**

(c)

Heat transfer at hot reservoir, Qh = 300 kW

Heat transfer at cold reservoir, Qc = 150 kW

Maximum net work -

Wcycle = Qh - Qc

Wcycle = 300 - 150 = 150 kW

Maximum efficiency -

ηmax = 1 - Tc/Th

ηmax = 1 - 500/1500 = 0.667

ηmax = 66.7%

η(actual) = Wcycle/ Qh

η(actual) = 150 kW/ 300 = 0.5

η(actual) = 50%

**Since the actual efficiency is lower than the maximum efficiency, the cycle operates irreversibly.**

(d)

Heat transfer at hot reservoir, Qh = 500 kW

Heat transfer at cold reservoir, Qc = 100 kW

Maximum net work -

Wcycle = Qh - Qc

Wcycle = 500 - 100 = 400kW

Maximum efficiency -

ηmax = 1 - Tc/Th

ηmax = 1 - 500/1500 = 0.667

ηmax = 66.7%

η(actual) = Wcycle/ Qh

η(actual) = 400 kW/ 500 = 0.8

η(actual) = 80%

**Since the actual efficiency is higher than the maximum efficiency, the cycle is not possible.**