C$1.$ You$$ve been given a $($cylindrical$)$ metal mass with some unknown heat capacity. You have liquid nitrogen available to you to cool the cylinder, and a beaker to fill with some amount $($your choice$)$ of water. Your goal is to predict the final temperature of the water, after the nitrogen$-$ cooled cube is added to it$.$ You are given that:

The latent heat of vaporization of nitrogen is $47\mathrm{.}8$ kcal$/$kg$=199,995\mathrm{.}2$ J$/$kg The density of liquid nitrogen is $808\mathrm{.}4$ kg$/$m$3$