A certain heat engine operating on a Carnot cycle absorbs $470$ JJ of heat per cycle at its hot reservoir at $145$C$$C and has a thermal efficiency of $24\mathrm{.}0\%\%.$ How much work does this engine do per cycle? How much heat does the engine waste each cycle? What is the temperature of the cold reservoir? By how much does the engine change the entropy of the world each cycle? What mass of water could this engine pump per cycle from a well $30\mathrm{.}0$ mm deep?