Model the electromagnetic wave in a microwave oven as a plane traveling wave moving to the left, with an intensity of 23.9 kw/m2. an oven contains two cubical containers of small mass, each full of water. one has an edge length of 6.18 cm, and the other, 11.2 cm. energy falls perpendicularly on one face of each container. the water in the smaller container absorbs 70.0% of the energy that falls on it. the water in the larger container absorbs 91.0%. that is, the fraction 0.300 of the incoming microwave energy passes through a 6.18-cm thickness of water, and the fraction (0.300)(0.300) = 0.090 passes through a 11.2-cm thickness. assume a negligible amount of energy leaves either container by heat. find the temperature change of the water in each container over a time interval of 468 s. (the density and the specific heat of water are 103 kg/m3 and 4 186 j/kg · °c, respectively.)

In a closed system, the total energy prior to an energy transformation is the total energy after. a. equal to b. unrelated to c. greater than d. less than

Classify the following soils according to the uscs classification system. provide appropriate uscs designations. a) this sample of well-graded gravel with sand was obtained from a large earthen dam in vancouver, canada. the sample has 73% fine to coarse sub-angular gravel, 25% fine to coarse sub-angular sand and 2% fines. the maximum size of the particles is 75 mm. the coefficient of curvature is 2.7, while the uniformity coefficient is 12.4. b) this dark brown and wet soil with a “strong organic odor” has 100% passing the no. 200 sieve. the liquid limit of the material is 32% when not dried and is 21% when oven-dried. the plastic index is 21% when not dried. c) this sand has 61% predominantly fine sand, 23% silty fines, and 16% fine sub-rounded gravel size. the maximum size is 20 mm. the liquid limit is 33% and the plastic limit is 27%. d) this soil has 74% fine to coarse sub-angular reddish sand and 26% organic and silty dark brown fines. the liquid limit is 37% when not dried and is 26% when oven dried. the plastic index is 6% when not dried.

Consider an insulating crystal, made up of layers of atoms. what form would you expect the temperature dependence of the phonon heat capacity to approach at extremely low temperatures if the interlayer coupling is i)very strong (rigid coupling), and ii) very weak. explain.