Problem $1$: Thermodynamics $-$ Gas Power Cycle

A gas turbine power plant operates on an ideal Brayton cycle with regeneration. The pressure ratio across the compressor is $10.$ Air enters the compressor at $300$ K and $100$ kPa and leaves at $800$ K$.$ The turbine inlet temperature is $1400$ K$,$ and the isentropic efficiencies of the compressor and turbine are $85\%$ and $90\%,$ respectively.

Determine the temperature and pressure at all points in the cycle.

Calculate the thermal efficiency of the cycle without regeneration.

If the regenerator effectiveness is $70\%,$ find the thermal efficiency of the cycle with regeneration.

Determine the back work ratio and the net work output per unit mass of air. What is Thermodynamics?.