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Liquid octane (C8H18) enters a steady-flow combustion chamber at 25oC and 1 atm at a rate of 0.25 kg/min. It is burned with 50 percent excess air that also enters at 25oC and 1 atm. After combustion, the products are allowed to cool to 25oC. Assuming complete combustion and that all the H2O in the products is in liquid form, determine

(a) The heat transfer rate from the combustion chamber

(b) The entropy generation rate

(c) The exergy destruction rate. Assume that T0 = 298 K and the products leave the combustion chamber at 1 atm pressure.

A homogeneous slab of thickness a is placed atop a fixed cylinder of radius R whose axis is horizontal. Show that the condition for stable equilibrium of the slab, assuming no slipping, is R > a/2. What is the frequency of small oscillations? Sketch the potential energy U as a function of the angular displacement ?. Show that there is a minimum at ? = 0 for R > a/2 but not for R < a/2.

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