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Consider a simple ideal Brayton cycle with air as the working fluid. The pressure ratio of the cycle is $6,$ and the minimum and maximum temperatures are $300$ and $1300$ K $,$ respectively. Now the pressure ratio is increased to $11\mathrm{.}00$ without changing the minimum and maximum temperatures in the cycle. Use data from the tables. Assume constant specific heats for air at room temperature. The properties of air at room temperature are $R=0\mathrm{.}287k\frac{J}{k}g*K,$

$c_p=l\mathrm{.}005k\frac{J}{k}g*K,c_v=0\mathrm{.}718k\frac{J}{k}g*K,$ and $k=1\mathrm{.}4$

Determine the difference in the thermal efficiency of the cycle as a result of increase in the pressure ratio.

The difference in the thermal efficiency of the cycle as a result of increase in the pressure ratio is $\%.$