I was running through some problems, doing just fine, until I came across these two. I can't work out a correct solution. 1) A 1-kg block of ice at 0 C falls into a lake whose water is also at 0 C, and 0.01 kg of the ice melts. What was the minimum altitude from which the ice fell? 2) Three designs for an engine to operate between 450 K and 300 K are proposed. Design A is claimed to require a heat input of 800 J for each 1000 J of work output, design B a heat input of 2500 J, and design C a heat input of 3500J. Which design would you choose and why?