Using a set of values from 0 to 5, perform the following unions using union-by-size. Show the result of each union. When sizes are the same, make the second tree a child of the first tree. Notice the finds return roots, and the union will union the roots. union(find(0),find(1)) union(find(3),find(4)) union(find(5),find(1)) union(find(2),find(5)) union(find(3),find(2)) 10 points

Thermal stresses are developed in a metal when its a) initial temperature is changed b) final temperature is changed c) density is changed d) thermal deformation is prevented e) expansion is prevented f) contraction is prevented

Awall of 0.5m thickness is to be constructed from a material which has average thermal conductivity of 1.4 w/mk. the wall is to be insulated with a material having an average thermal conductivity of 0.35 w/mk so that heat loss per square meter shall not exceed 1450 w. assume inner wall surface temperature of 1200°c and outer surface temperature of the insulation to be 15°c. calculate the thickness of insulation required.

Air is compressed isentropically from an initial state of 300 k and 101 kpa to a final temperature of 1000 k. determine the final pressure using the following approaches: (a) approximate analysis (using properties at the average temperature) (b) exact analysis