A reciprocating internal combustion engine is required to operate on land at an altitude of $3$ km above sea level $($ASL$).$ In order to improve the engine performance at such a high altitude, it is equipped with a turbocharger and intercooler, as shown in Figure $4-$Legend $1$: Ambient conditions $/$ compressor inlet $2$: Compressor exit $/$ intercooler inlet $3$: Intercooler exit $/$ engine intake $4$: Engine exhaust $/$ turbine inlet $5$: Turbine exit,The following specifications applicable to the turbocharger, intercooler and engine are known: Compressor pressure ratio $1,65$:$1$ Compressor isentropic efficiency: $72\%$ Intercooler pressure drop, relative to P$2$: $2\%$ Intercooler exit temperature: $10\%$ above T$1$ Engine air$-$fuel ratio: $15$:$1$ Mechanical efficiency of turbocharger shaft: $98\%$ Turbine inlet temperature: $800$ K Turbine isentropic efficiency: $80\%$ Calculate the following ambient$-,$ turbocharger$-$ and intercooler parameters: Q$\mathrm{.}4\mathrm{.}1$ Ambient pressure P$1$ and temperature T$1$ at an altitude of $3$ km above sea level. $(2)$ Q$\mathrm{.}4\mathrm{.}2$ Compressor: Delivery pressure and temperature, as well as specific shaft work. $(14)$ Q$\mathrm{.}4\mathrm{.}3$ Intercooler: Delivery pressure and temperature, as well as specific cooling capacity. $(9)$ Q$\mathrm{.}4\mathrm{.}4$ Turbine: Delivery pressure and temperature, as well as pressure ratio. $(10)$ The following specifications applicable to the turbocharger, intercooler and engine are known:

Calculate the following ambient$-,$ turbocharger$-$ and intercooler parameters:

Q$\mathrm{.}4\mathrm{.}1$ Ambient pressure $\backslash ($ P$\_\{1\}\backslash )$ and temperature $\backslash ($ T$\_\{1\}\backslash )$ at an altitude of $3$ km above sea level.

Q$\mathrm{.}4\mathrm{.}2$ Compressor: Delivery pressure and temperature, as well as specific shaft work.

Q$\mathrm{.}4\mathrm{.}3$ Intercooler: Delivery pressure and temperature, as well as specific cooling capacity.

Q$\mathrm{.}4\mathrm{.}4$ Turbine: Delivery pressure and temperature, as well as pressure ratio.