An air$-$conditioning system operates at a total pressure of $100$ kPa and consists of a heating section and a humidifier that supplies wet steam $($saturated water vapor$)$ at $100.$ Air enters the heating section at $10.$and $60$ percent relative humidity at a rate of $1$ kg$/$s$,$ and it leaves the humidifying section at $20.$ and $50$ percent relative humidity. Determine

$($a$)$ the temperature and relative humidity of air when it leaves the heating section,

$($b$)$ the rate of heat transfer in the heating section, and

$($c$)$ the rate at which water is added to the air in the humidifying section.