Q$1)$ A window air conditioner using R$-134$a is rated at $24,000Bt\frac{u}{h}r$ when operating between an evaporative temperature of $40$ F and a condensing temperature of $125$F$.$ A thermostatic expansion valve is used so that the refrigerant vapor leaving the evaporator is superheated by $20F$ to safeguard against any liquid entering the compressor. If the compressor efficiency is $62\%,$ determine: the adiabatic discharge temperature from the compressor $($F$)$: $(25\%)$

$($a$)$ The adiabatic discharge temperature from the compressor $(F)$

$($b$)$ The power input $($kW$)$

$($c$)$ Clearly show the cycle on the P$-$H Diagram $($see on LSATE$).$