$(30$ points$)$ Concentrated Solar Power $($CSP$)$ Plant

CSP is a proven means of solar power generation and new technologies are lowering its cost curve, but a common characteristic of current CSP technologies is the use of steam turbines for power generation. Steam turbines, although well understood, consume large amounts of water and require extensive balance$-$of$-$plant equipment. CSP works best in regions with a lot of sun year$-$round, and these tend to be desert areas where water is in short supply and permission to use water may be difficult or impossible to obtain.

The Brayton cycle provides an attractive alternative because it only utilizes air. Consider the following Brayton cycle. Air enters the compressor at $100$ kPa and $300$ K and is compressed to $1\mathrm{.}67$ MPa $.$ As the air passes through the solar receiver device it is heated at a rate $Q_{in}^{}=2525$ kW $.$ The heated air then expands through the turbine and is exhausted. The isentropic efficiency of the compressor is $87\%$ and the isentropic efficiency of the turbine is $89\%.$ The mass flow rate through the cycle is $m^{}=5k\frac{g}{s}.$

$($c$)(15$ points$)$ Determine the electrical power output $($it is not necessary to interpolate unless the table value of a reference state is different by more than $1$ percent$)$