Consider a two-dimensional triangular lattice described by the two primitive vectors (in an orthogonal coordinate system) ~a1 = a(1, 0) ; ~a2 = a 1 2 , √ 3 2 ! find the two primitive lattice vectors ~b1, ~b2 describing the reciprocal lattice. find the area of the 1st brillouin zone and find its relation with the area of the direct lattice unit cel

Acommercial grade cubical freezer, 4 m on a side, has a composite wall consisting of an exterior sheet of 5.0-mm thick plain carbon steel (kst= 60.5 w/m k), an intermediate layer of 100-mm thick polyurethane insulation (kins 0.02 w/m k), and an inner sheet of 5.0- mm thick aluminium alloy (kal polyurethane insulation and both metallic sheets are each characterized by a thermal contact resistance of r 2.5 x 104 m2 k/w. (a) what is the steady-state cooling load that must be maintained by the refrigerator under conditions for which the outer and inner surface temperatures are 25°c and -5°c, respectively? (b) for power saving purpose, which wall material should be increased/reduced in. thickness in order to reduce 50% of the cooling load found in part (a)? redesign the thickness of the proposed material. 177 w/m-k). adhesive interfaces between the q=575.93 w