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Problem $10\mathrm{.}128-$ Multi$-$stage regenerative Brayton Cycle

Consider an ideal gas$-$turbine cycle with two stages of compression and two stages of expansion. The pressure ratio

across each stage of the compressor and turbine is $3.$ The air enters each stage of the compressor at $300$ K and each

stage of the turbine at $1200$ K$.$ Use variable specific heats.

Problem $10\mathrm{.}128.$b $-$ Ideal Gas$-$Turbine Cycle with $2-$stage compression and expansion with regeneration

Determine the back work ratio and the thermal efficiency of the cycle, assuming a regenerator with $77\mathrm{.}0$ percent effectiveness is used.

The back work ratio is

$.$

The thermal efficiency is

$\%.$