In an ideal Joule-Brayton cycle operating between fixed compressor inlet temperature $T_1$ and turbine inlet temperature $T_3$, the pressure ratio that maximizes net cycle specific work is:

(A) $r_p = \left(\frac{T_3}{T_1}\right)^{\frac{\gamma}{2(\gamma - 1)}}$

(B) $r_p = \left(\frac{T_3}{T_1}\right)^{\frac{\gamma}{\gamma - 1}}$

(C) $r_p = 1.0$

(D) $r_p = \sqrt{\frac{T_3}{T_1}}$

Answer Key:

A

### Solution: Net specific work $w_{net} = c_p (T_3 - T_4 - (T_2 - T_1))$. Differentiating with respect to temperature ratio yields optimum $r_p = (T_3/T_1)^{\frac{\gamma}{2(\gamma-1)}}$. Correct: A.

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