MECH 310 Exam 2, Fall 2010

MECH 310 Thermodynamics I American University of Beirut, Fall 2010 January 15, 2011 Handout # Qviz 2 Quiz 2 Problem 1 (40 points) Consicler a two story storage buiiding. The first fl.oor is maintained at iow temperature 72, such lhat T1< 4 and the second floor is maintained at a high temperature 7s such that Ta ) To, where Q is the ambient temperature. The upper floor loses heat steadily to the both the environment and the lower floor. In addition, the lower fl.oor also gain heat steadily from the environment and the upper floor. Evaluate each of the following two scenarios for heating the upper floor and cooling the lower floor in terms of the minimum possible cost (rate of work consumed): (a) The heat rate lost by the upper floor is compensateci by electric heating and that gained by the iower floor is removed using a refrigeration cyclic engine operating between the lower floor and the environment. (b) Same as in (a) except that instead of electrically heating the upper floor, we employ a heat pump operating between the upper floor and the environment. (c) Can you do better than (a) and (b) to achieve lower rate of work consumption. Sketch your solution including all the heat engines, heat pumps and refrigeration cycles you employ. Q,*r-*Q*q t fsrru Qnu. W7 scenalio (a) *Q*") TrJ tL scenario (b) a b-,'** -'lw;n e" Problem 2 (30 points) A simple steam power plant operates at sjsdystate with water circulating through com- ponents with a mass flow rate of 60 kgfs. Figure 2 shows additional data at key points in the cycle. Stray heat transfer and kinetic and potential effects are negiigible. Determine (a) the thermal efficiency (b) the mass flow rate of cooling water through the condenser, in kg/s. Pr :3 MPa Tr:400oC cooling water in cooling water out Ta:Ts+15"C Figure 3 Problem 3 (30 points) A well insulated piston-cylinder assembly is connected by a valve to an air suppiy line at 500 K and 8 bar, as shown in Figure 3. Initially the air inside the cylinder is at 1.1 bar, 300 K, and the piston is located 0.5 m above the bottom of the cylinder. The atmospheric pressure is 1 bar, and the diameter of the piston face is 0.3 m. The valve is opened and air is admitted slowly until the volume of air inside the cylinder has doubled. The friction between the piston and the cylinder wall can be ignored. (a) Find the finai temperature in oK. (b) Find the final mass in kg. (c) What are the final temperature and mass if the air supply line is at 6 bar. we C-- L,.\e us f4'V )f v Figure 2 r^rVr +\nrJt,- - s1$r -s,11, + nnf3({r-t,\ *q: -,o -o*tt '(r^'1g I tt:) = rs\ s' ) --!. D--^ - $F 0 r$ Y.A Initially: .Lt :0.5 m Tr=300K Pr : 1.1 bar Ta:82"C Pa:50 kPa