A perfectly insulated container initially contains 0.2 kg of ice at -15 C. Now we add water at 30 C, but only the minimum amount needed to barely melt all the ice. Find the net entropy change of the universe. Possible relevant quantities: Ice heat capacity 2100 J/(kg) (K); water heat capacity 4190 J/(kg)(K); HO latent heat of fusion 334,000 J/(kg)(K); HO latent heat of vaporization 2,256,000 J/(kg)(K) A Carnot cycle operates with the bottom of the ocean (temperature 0 C) as its cold reservoir and the surface of the ocean (temperature 20 C) as its hot reservoir. The engine generates 250 J of work per cycle. Find the entropy change in the bottom of the ocean for each cycle. You have a MONATOMIC gas initially at volume Vo and pressure Po (which you can take as given quantities). You now expand it to 9 times the initial volume, using the process P=PoVo/V. (a) Show that the final temperature is 3 times the initial temperature. [10 points] (b) On a PV diagram, show the isotherms at the initial and final temperature (as dotted lines) and the process connecting them (as a solid line with a direction arrow). [10 points] (c) Find the molar heat capacity for this process (you should get an actual number) Hint: Try calculating the heat using the first Law of Thermodynamics. [25 points]