The gram–schmidt process for constructing an orthogonal set that was discussed in section 7.7 carries over to a linearly independent set { f0(x), f1(x), f2(x), …} of real-valued functions continuous on an interval [a, b]. with the inner product ( fn, fn) eb a fn(x)fn(x) dx, define the functions in the set b9 5f0(x), f1(x), f2(x), p 6 to be f0(x) f0(x) f1(x) f1(x) 2 ( f1, f0) (f0, f0) f0(x) f2(x) f2(x) 2 ( f2, f0) (f0, f0) f0(x) 2 ( f2, f1) (f1, f1) f1(x) o o and so on. (a) write out f3(x) in the set. (b) by construction, the set b9 5f0(x), f1(x), f2(x), p 6 is orthogonal on [a, b]. demonstrate that f0(x), f1(x), and f2(x) are mutually orthogonal.

Amass of m 1.5 kg of steam is contained in a closed rigid container. initially the pressure and temperature of the steam are: p 1.5 mpa and t 240°c (superheated state), respectively. then the temperature drops to t2= 100°c as the result of heat transfer to the surroundings. determine: a) quality of the steam at the end of the process, b) heat transfer with the surroundings. for: p1.5 mpa and t 240°c: enthalpy of superheated vapour is 2900 kj/kg, specific volume of superheated vapour is 0. 1483 m/kg, while for t 100°c: enthalpy of saturated liquid water is 419kj/kg, specific volume of saturated liquid water is 0.001043m/kg, enthalpy of saturated vapour is 2676 kj/kg, specific volume of saturated vapour is 1.672 m/kg and pressure is 0.1 mpa.

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

The filament of an incandescent lamp has a temperature of 2000k. calculate the fraction of radiation emitted in the visible light band if the filament is approximated as blackbody