A heat engine uses steam as the working fluid. The thermal efficiency is $30\%$ and rejects heat at the rate of $1,000k\frac{J}{k}g.$ Determine $($i$)$ the heat that must be received if a $50$ MW power plant is to be designed, $($ii$)$ the mass flow rate of steam required, and $($iii$)$ COP. $($Watch "heat pump cycle$2"$ or DS$)$