Question: A gas turbine engine operates between minimum temperature (T_{1}) and maximum temperature (T_{3}). Show that the optimum pressure ratio for maximum work output is [r_{p}=left(frac{T_{3}}{T_{1}}

A gas turbine engine operates between minimum temperature $T_{1}$ and maximum temperature $T_{3}$. Show that the optimum pressure ratio for maximum work output is

\[r_{p}=\left(\frac{T_{3}}{T_{1}}\right)^{\frac{\kappa}{2(\kappa-1)}}\]

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