Answer
a) $C=\$1.85/year$
b) $C=\$0.96/year$
Work Step by Step
$V_{air}=0.3\ m³/open\times 20\ open/day\times 365\ days/year=2190\ m³/year$
$PV=mRT,\ R=0.287\ kJ/kg.K,\ T=4°C,\ P=95\ kPa$
$m_{air}=2617\ kg$
$Q_{air}=m_{air}c_p\Delta T, c_p=1.005\ kJ/kg.°C,\ \Delta T=(20-4)°C=16°C$
$Q_{air}=42.082\ MJ/year$
$m_{moist}=0.006m_{air}$
$m_{moist}=15.7\ kg/year$
$Q_{moist}=m_{moist}\Delta h_v,\quad \Delta h_v=2491.4\ kJ/kg$
$Q_{moist}=39.121\ MJ/year$
$Q=Q_{moist}+Q_{air}$
$Q=81.2\ MJ/year$
$E=Q/COP,\ COP=1.4$
$E=16.11\ kWh/year$
$C=E\times p,\ p=\$0.11/kWh$
$C=\$1.85/year$
Redoing the last steps if $Q=Q_{air}$:
$E=8.35\ kWh/year$
$C=\$0.96/year$
