A power cycle operating at steady state is shown below. Net power output of the cycle is $29,830kW.$ Air

enters a well$-$insulated low$-$pressure compressor $($LPC$)$ at an absolute pressure of $100$ kPa and an absolute

temperature of $300$ K $($State $1)$ and is compressed to an absolute pressure of $300$ kPa and an absolute

temperature of $420$ K $($State $2).$ Air leaving the LPC is cooled through a rigid intercooler to an absolute

pressure of $300$ kPa and an absolute temperature of $300$ K $($State $3).$ Air then enters an adiabatic high$-$

pressure compressor $($HPT$)$ and is compressed to an absolute pressure of $1200$ kPa and an absolute

temperature of $460$ K $($State $4).$ Air is heated to an absolute pressure of $1200$ kPa and an absolute

temperature of $1120$ K $($State $5)$ using energy from another air stream passing through a rigid and externally

well$-$insulated regenerator. Air is further heated to an absolute pressure of $1200$ kPa and an absolute

temperature of $1500$ K $($State $6)$ using a rigid combustor. Air enters an adiabatic high$-$pressure turbine

$($HPT$)$ and expands to an absolute pressure of $300$ kPa and an absolute temperature of $1100$ K $($State $7).$ Air

leaving the HPT is heated to an absolute pressure of $300$ kPa and an absolute temperature of $1500$ K $($State

using another rigid combustor. Air then expands through a well$-$insulated low$-$pressure turbine $($LPT$)$ to

an absolute pressure of $100$ kPa and an absolute temperature of $1160$ K $($State $9).$ Air leaving the LPT then

passes through the regenerator and exits at an absolute pressure of $100$ kPa $($State $10).$

$($a$)$ Calculate the mass flow rate of air in the cycle, in $k\frac{g}{s}.$

$($b$)$ Determine the absolute temperature of air at State $10,$ in K$.$

$($c$)$ Find the rate of heat transfer into the cycle, in kW $.$

$($d$)$ Find the thermal efficiency of the power cycle, in $\%.$