A power cycle receives QH by heat transfer from a hot reservoir at TH = 1200 K and rejects energy QC by heat transfer to a cold reservoir at TC = 400 K. For each of the following cases, determine whether the cycle operates reversibly, operates irreversibly, or is impossible. a. QH = 900 kJ, Wcycle= 450 kJ
b. QH = 900 kJ, Qc = 300 kJ
c. Weycle = 600 kJ, Qc= 400 kJ
d. η = 75%

a) Irreversible, b) Reversible, c) Irreversible, d) Impossible.

Explanation:

Maximum theoretical efficiency for a power cycle (), no unit, is modelled after the Carnot Cycle, which represents a reversible thermodynamic process:

(1)

Where:

- Temperature of the cold reservoir, in Kelvin.

- Temperature of the hot reservoir, in Kelvin.

The maximum theoretical efficiency associated with this power cycle is: (, )

In exchange, real efficiency for a power cycle (), no unit, is defined by this expression:

(2)

Where:

- Heat released to cold reservoir, in kilojoules.

- Heat gained from hot reservoir, in kilojoules.

- Power generated within power cycle, in kilojoules.

A power cycle operates irreversibly for , reversibily for and it is impossible for .

Now we proceed to solve for each case:

a) ,

Since , the power cycle operates irreversibly.

b) ,

Since , the power cycle operates reversibly.

c) ,

Since , the power cycle operates irreversibly.

d) Since , the power cycle is impossible.