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