Given an instance (s, k) of the subset-sum problem, where s is a set of integers and k is another integer, we transform it into an instance s’ = s ∪ { x, y } of the partition problem, where x = sum(s) + k, y = 2sum(s) – k, and sum(s) = σx∈s x. prove that s’ can be constructed from s in polynomial time and there exists a subset x ⊆ s’ such that sum(x) = k iff s’ can be partitioned into x and y such that sum(x) = sum(y), where s’ = x∪y and x∩y = ∅

The drive force for diffusion is 7 fick's first law can be used to solve the non-steady state diffusion. a)-true b)-false

Consider a large isothermal enclosure that is maintained at a uniform temperature of 2000 k. calculate the emissive power of the radiation that emerges from a small aperture on the enclosure surface. what is the wavelength ? , below which 10% of the emission is concentrated? what is the wavelength ? 2 above which 10% of the emission is concentrated? determine the wavelength at which maximum spectral emissive power occurs. what is the irradiation incident on a small object placed inside the enclosure?

An ideal otto cycle with air as the working fluid has a compression ratio of 8. the minimum and maximum temperatures in the cycle are 300 k and 1340 k. use constant specific heats at room temperature to determine (a) the amount of heat transferred to the air during the heat- addition kj/kg, (b) the thermal efficiency, and (c) the thermal efficiency of a carnot cycle ope limits. process, in rating between the same temperature