The steady-state data listed below are claimed for a power cycle operating between hot and cold reservoirs at 1200 K and 400 K, respectively. For each case, evaluate the net power developed by the cycle, in kW, and the thermal efficiency. Also in each case apply the equation below on a time-rate basis to determine whether the cycle operates reversibly, operates irreversibly, or is impossible.
(a) Qh(dot)=600 kW, Qc(dot)=400 kW
(b) Qh(dot)=600 kW, Qc(dot)=0 kW
(c) Qh(dot)=600 kW, Qc(dot)=200 kW

∮ (δQ/T)_b = -σ_cycle

(a) Qh(dot)=600 kW, Qc(dot)=400 kW  is an irreversible process.

(b) Qh(dot)=600 kW, Qc(dot)=0 kW  is an impossible process.

(c) Qh(dot)=600 kW, Qc(dot)=200 kW  is a reversible process.

Explanation:

T(hot) = 1200k, T(cold) = 400

efficiency n = (Th - Tc ) / Tc

n = (1200 - 400) / 1200 = 0.667 (this will be the comparison base)

(a)

Qh = 600 kW, Qc = 400 kW

n = (Qh - Qc) / Qh ⇒ (600 - 400) / 600

n = 0.33

0.33 is less than efficiency value from temperature 0.67

∴ it is irreversible process

(b)

Qh = 600 kW, Qc = 0

n = (Qh - Qc) / Qh ⇒ (600 - 0) / 600 = 1

efficiency in any power cycle can never be equal to one.

∴ it is an impossible process.

(c)

Qh = 600 kW, Qc = 200 kW

n = (Qh - Qc) / Qh = (600 - 200) / 600

n = 0.67 (it is equal to efficiency value from temperature)

∴ it is a reversible process

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