An air conditioning plant consists of dehumidifier and heater section. The fan delivers $5k\frac{e}{s}$ of moist air from the inlet to the dehumidifier. The condition of the entry air is $1\mathrm{.}5$ bar pressure, $38C$ temperature and $0\mathrm{.}88$ relative humidity. The air is required to leave the air conditioning plant at the condition of $1$ bar pressure, $12C$ temperature and $0\mathrm{.}5$ relative humidity. The pressure of the air$-$vapor mixture is $1\mathrm{.}3$ bar at exit from the dehumidifier, determine the cooling duty and the heating duty. $(20)$