Atrivial oz code for returning the number of elements of a list can be given by: declare fun {length l} case l of nil then 0 [] h|t then 1+{length t} end end for example, the call {browse {length [1 f 2 3 s 5]}} will display 6. explain why this function is not tail recursive. write an equivalent tail recursive function. write also an invariant for this tail recursive function. using the invariant, prove the correctness for this program.

Apiston-cylinder with a volume of 0.25 m3 holds 1 kg of air (r 0.287 k/kgk) at a temperature of 100 c. heat transfer to the cylinder causes an isothermal expansion of the piston until the volume triples. how much heat is added to the piston-cylinder?

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?

Draw the engineering stress-strain curve for (a) bcc; (b) fcc metals and mark important points.