Question $15(3$ points$)$

$i,$

The stationary system below shows a hot water container with the square cross section $1\mathrm{.}5m1\mathrm{.}5m,$ having the temperature of $90C,$ is cooled by the cold air at the temperature of $10C,$ while being stirred by the paddle wheel rotating with the torque of $550N.m.$ If the heat transfer coefficient between the water and the coolant is $250\frac{W}{m^2}C$ and the loss in the internal energy during the process is $30kW$; determine:

$1-$ The work done by the paddle wheel on the water

$2-$ The rotation speed $($rpm$)$ of the paddle wheel