Exam 2 - K . 3. (50) Consider the Rankine cycle below. ind...

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NAME: AME 20231 Thermodynamics Examination 2 Prof. J. M. Powers 31 March 2010 Happy 156th birthday, Sir Dugald Clerk, inventor of the two-stroke engine, b. 31 March 1854. 1. (25) A calorically imperfect ideal gas, with gas constant R and initially at P 1 , T 1 , V 1 , Flls a cylinder which is capped by a frictionless mobile piston. The gas is heated until V = V 2 . The speciFc heat is given by c v ( T ) = c vo + αT, where c vo and α are constants. ±ind the Fnal temperature and the heat transferred to the gas in terms of given quantities. 2. (25) A sphere of aluminum with radius of 0 . 01 m is initially at 1500 K . It is suddenly immersed in a very large tub of water at 300 K . The heat transfer coe²cient is h = 10 kW/m 2 /K . Assuming the sphere has a spatially uniform temperature and constant material properties, Fnd the time when the sphere’s temperature is 400
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Unformatted text preview: K . 3. (50) Consider the Rankine cycle below. ind boiler turbine condenser 3 4 1 2 P 3 = 15 MPa T 3 = 400 C P 4 = 10 kPa x 4 = 1 P 1 = 10 kPa x 1 = 0 m = 100 kg/s . cold lake water in warm lake water out, T = 20 C pump P 2 = 15 MPa T 2 = 60 C heat loss from non-adiabatic turbine = 5000 kW (a) the heat transfer rate to the boiler ( kW ), (b) the power output of the turbine ( kW ), (c) the overall thermal eciency, (d) the thermal eciency of a Carnot cycle operating between the same temperature limits, (e) an accurate sketch of the cycle on a T-s diagram, (f) the mass ow rate of external lake cooling water to exchange heat with the condenser if the lake cooling water temperature rise is designed to be 20 C ....
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