Assume that a chocolate bar consists of n squares ar- ranged in a rectangular pattern. The entire bar, or any smaller rectangular piece of the bar, can be broken along a vertical or a horizontal line separating the squares. Assuming that only one piece can be broken at a time, determine how many breaks you must successively make to break the bar into n separate squares. Use strong in- duction to prove your answer.

Agas contained within a piston-cylinder assembly e end nation about same energy states, 1 and 2, where pi 10 bar, v undergoes two processes, a and b, between the sam 0.1 m3, ui-400 kj and p2 1 bar, v2 1.0 m2, u2 200 kj: process a: process from 1 to 2 during which the pressure- volume relation is pv constant process b: constant-volume process from state 1 to a pressure of 2 bar, followed by a linear pressure-volume process to +20 0 state 2 kinetic and potential energy effects can be ignored. for each of the processes a and b, (a) sketch the process on p-v coordinates, (b) evaluate the work, in kj, and (c) evaluate process the heat transfer, in kj