Show that the decision version of the knapsack problem is np-complete. (hint: in your reduction, make use of the partition problem: given n positive integers, partition them into two disjoint subsets with the same sum of their elements. the partition problem is np-complete.)

Carbon dioxide gas expands isotherm a turbine from 1 mpa, 500 k at 200 kpa. assuming the ideal gas model and neglecting the kinetic and potential energies, determine the change in entropy, heat transfer and work for each kilogram of co2.

Aquick transition of the operating speed of a shaft from its critical speed will whirl amplitude. (a) increase (b) limit (c) not affect (d) zero

Acarnot refrigerator operates in a room in which the temperature is 21°c and of power when operating. if the food compartment of the refrigerator is consumes 3 kw to be maintained at 2°c, determine (a) the coefficient of performance of the cycle and (b) the rate of heat removal from the food compartment. refrigerator cycle that has a higher coefficient of performance than that of the discussed (e) is it possible to develop a carn ot refrigerator, operating between the same temperature limits? explain