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Final Exam-Solution - CHEMICAL ENGINEERING T HERMODYNAMICS...

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CHEMICAL ENGINEERING THERMODYNAMICS I (ChBE 2110) Fall 2008, Final 1. (10 points) A stream of air at atmospheric pressure is cooled continuously from 38 o C to 15 o C for purposes of air-conditioning a building. The temperature of the ambient air to which heat is discarded is 38 o C. What is the minimum power requirement of a mechanical refrigeration system designed to accomplish the necessary cooling? It is known that volumetric flow is 0.5 m 3 s -1 (measured at 25 oC) and air can be treated as ideal gas. C P = 7/2 R is independent on temperature. The potential and kinetic-energy change is negligible. Solution: From the energy balance (see the Figure) Q W H H H S in out + = - = 1 1 2 3 . 669 ) 15 . 311 15 . 288 )( 314 . 8 ( 2 7 ) ( - - = - = - = Jmol T T C H P To obtain the biggest efficiency, the devise must be reversible, so Q = T S 1 1 1 2 2346 . 2 15 . 311 15 . 288 ln ) 314 . 8 ( 2 7 ln - - - = = = K Jmol T T C S P [ ] W W n W 2 . 531 ) 2346 . 2 ( 15 . 311 ) 3 . 669 ( 44 . 20 - = - × - - × = = Control system Air at 38 o C Air at 15 o C s W Q Surroundings at 38 o C
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2. (15 points) Water at 40 oC and 10 kPa is pumped adiabatically from the condenser of a power plant to the boiler pressure of 7200 kPa. If the pump is 80% efficient compared with reversible (isentropic) operation, find (a) the work required and (b) the temperature rise of water.
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