Question

In a Brayton cycle, the maximum and minimum temperatures are 1600 K and 300 K. If the ratio of specific heats for the working fluid is 1.67, the product of pressure ratio corresponding to maximum work output and maximum efficiency is ______

• A. 522.52

Answer 1

The correct option is A 522.52
For maximum work output,

$({\tau }_P{)}_{MW}={\left(\frac{T_{max}}{T_{min}}\right)}^{\frac{\gamma }{2(\gamma -1)}}$

For maximum efficiency,

$({\tau }_P{)}_{ME}={\left(\frac{T_{max}}{T_{min}}\right)}^{\frac{\gamma }{\gamma -1}}$

$({\tau }_P{)}_{MW}\times ({\tau }_P{)}_{ME}={\left(\frac{T_{m}ax}{T_{min}}\right)}^{\frac{3\gamma }{2(\gamma -1)}}=\left({\frac{1600}{300}}^{\frac{3\times 1067}{2(1067-1)}}\right)=522.52$