Describe and analyze a data structure to support the following operations on an array a[1 . . n] as quickly as possible. initially, a[i] = 0 for all i. • settoone(i) given an index i such that a[i] = 0, set a[i] to 1. • getvalue(i) given an index i, return a[i] • getclosestrightzero(i) given an index i, return the smallest index j ≥ i such that a[j] = 0, or report that no such index exists. the first two operations should run in worst-case constant time, and the amortized cost of the third operation should be as small as possible. 3

An air conditioning system consist of a 5 cm diameter pipe, operating at a pressure of 200 kpa. the air initially enters the pipe at 15°c with a velocity of 20 m/s and relative humidity of 80%. if the heat supply throughout the process is 960 w, determine the relative humidity and the temperature at the outlet

Air is to be cooled in the evaporator section of a refrigerator by passing it over a bank of 0.8-cm-outer-diameter and 0.4-m-long tubes inside which the refrigerant is evaporating at -20°c. air approaches the tube bank in the normal direction at 0°c and 1 atm with a mean velocity of 4 m/s. the tubes are arranged in-line with longitudinal and transverse pitches of sl- st 1.5 cm. there are 30 rows in the flow direction with 15 tubes in each row. determine (a) the refrigeration capacity of this system and (b) pressure drop across the tube bank. evaluate the air properties at an assumed mean temperature of -5°c and 1 atm. is this a good assumption?

Slip occurs via two partial dislocations because of (a) the shorter path of the partial dislocation lines; (b) the lower energy state through partial dislocations; (c) the charge balance.