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The diagram shows a conical section fabricated from pyroceram. It is of circular cross section with the diameter D = ax, where a = 0.25. The small end is at x, = 50 mm and the large end at x2 = 250 mm. The end temperatures are 7, = 400 K and 72 = 600 K, while the lateral surface is well insulated. 12 1. Derive an expression for the temperature distribution 7(x) in symbolic form, assuming one-dimensional conditions. Sketch the temperature distribution. 2. Calculate the heat rate q, through the cone.A firefighter's protective clothing, refered to as a furnout coat, is typically constructed as an ensemble of three lay- ers separated by air gaps, is shown schematically. -Shall It Thannal barring I'mby Firm-aids Arup Representative dimensions and thermal conductivitys for the layers are as follows. Lower Thickness imm) &(W/m . K) Shell (s) (1047 Moisture barrier (mb) 055 01012 Thermal liner full 35 The air gaps between the layers are I mm thick, and heat is transferred by conduction and radiation exchange through the stagnant air. The linearized radiation coefficient for a gap may be approximated is, hol+ +idol , where represents the average temperature of the surfaces comprising the gap, and the radiation flux across the gap may be expressed is qu = he(7 - Ty. (a) Represent the turnout coat by a thermal circuit, labeling all the thermal resistances. Calculate and tabulate the thermal resistances per unit area (m- K/W) for each of the layers, as well as for the con- duction and radiation processes in the gaps. Assume that a value of T_= 470 K may be used to approx- imare the radiation resistance of both pops. Com- ment on the relative magnitudes of the resistances. (b) For a pre-ask-over fire environment in which fire- fighters often work, the typical radiant heat flux on the fire-side of the turnout coat is 0.25 Wiem".To get started in a new telecommuting position with AB Hammond Engineers, Jane took out a $1000 loan at i = 10% per year for 4 years to buy home office equipment. From the lender's perspective, the investment in this young engineer is expected to produce an equivalent net cash flow of $315.47 for each of 4 years. A = $1000(4/P,10%,4) = $315.47 This represents a 10% per year rate of return on the unrecovered balance. Compute the amount of the unrecovered investment for each of the 4 years using (a) the rate of return on the unre- covered balance (the correct basis) and (b) the return on the initial $1000 investment. (c) Ex- plain why all of the initial $1000 amount is not recovered by the final payment in part (b).\fA study was conducted by the Department of Zoology at Virginia Tech to determine if there is a signicant difference in the density of organisms at two different stations located on Cedar Run, a secondary stream in the Roanoke River drainage basin. Sewage from a sewage treatment plant and overflow from the Federal Mogul Corporation settling pond enter the stream near its headwaters. The following data give the density measurements, in number of organisms per square meter, at the two collecting stations: Number of Organisms per Square Meter Station 1 Station 2 5030 4080 2800 2810 13,?00 11,010 4670 1330 10, T30 8130 6890 3320 11,400 26,850 7720 1230 860 17,660 7030 2130 2200 22,800 7330 2190 4250 1 130 15,040 1690 Can we conclude, at the 0.05 level of significance, that the average densities at the two stations are equal? Assume that the observations come from normal populations with different variances. \f