$2\mathrm{.}1.$ A nonconducting container filled with $25$ kg of water at $20C$ is fitted with a stirrer, which is made to turn by gravity acting on a weight of mass $35$ kg $.$ The weight falls slowly through a distance of $5$ m in driving the stirrer. Assuming that all work done on the weight is transferred to the water and that the local acceleration of gravity is $9\mathrm{.}8m*s^{-2},$ determine:

$($a$)$ The amount of work done on the water.

$($b$)$ The internal energy change of the water.

$($c$)$ The final temperature of the water, for which $C_P=4\mathrm{.}18kJ*k{g}^{-1}*C^{-1}.$

$($d$)$ The amount of heat that must be removed from the water to return it to its initial temperature.

$($e$)$ The total energy change of the universe because of $(1)$ the process of lowering the weight, $(2)$ the process of cooling the water back to its initial temperature, and $(3)$ both processes together.