Problem $1$:

A two$-$stage compressor in a gas turbine brings atmospheric air at $100$kPa,$17C$ to $500$ kPa $,$ then cools it in an intercooler to $27C$ at constant $P.$ The second stage brings the air to $1000$ kPa $.$ Assume both stages are adiabatic and reversible. Find the combined specific work to the compressor stages. Compare that to the specific work for the case of no intercooler $($i$.$e$.$ one compressor from $100$ to $1000$ kPa $).$

Problem $2$:

Consider an ideal gas$-$turbine cycle with two stages of compression and two stages of expansion. The pressure ratio across each compressor stage and each turbine stage is $8$ to $1.$ The pressure at the entrance to the first compressor is $100$ kPa $,$ the temperature entering each compressor is $20C,$ and the temperature entering each turbine is $1100C.$ An ideal regenerator is also incorporated into the cycle. Determine the compressor work, the turbine work, and the thermal efficiency of the cycle. Use the cold air properties $($i$.$e$.$ constant heat capacities at $20C).$