$5\mathrm{.}7$ A basic, standard air gas turbine has a compressor inlet temperature and pressure of $530$ R and $14\mathrm{.}7$ psi abs$.,$ respectively, a compressor outlet and turbine inlet pressure of $231\mathrm{.}5$ psi abs$.,$ a turbine inlet temperature of $2520$ R$,$ a turbine outlet pressure of $14\mathrm{.}7$ psi abs$.,$ a compressor efficiency of $82\%,$ and a turbine efficiency of $85\%.$ Air enters the compressor at a rate of $100$ lb$/$s$.$ Calculate, assuming that specific heats are variable:

a$)$ The power required to drive the compressor.

b$)$ The fraction of the work performed by the turbine that is required to drive the compressor.

c$)$ The power that the turbine can deliver to an external generator.