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Exam%201_Solutions

# Exam%201_Solutions - ChBE 321 Chemical Engineering...

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ChBE 321 – Chemical Engineering Thermodynamics Exam #1 – February 15th, 2008 Name: ANSWER KEY 2:00 PM-2:50 PM Answer all questions in this answer sheet. You will have 50 minutes to complete this exam. Ask for clarification if a question is unclear. This exam is open notes and open textbook. There are three questions on this exam. Inspect exam to ensure it is complete. 1

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ChBE 321 – Chemical Engineering Thermodynamics Exam #1 – February 15th, 2008 Problem 1. For all parts of this problem, assume no frictional losses. (a) An ideal gas is confined in a 2-meter-diameter cylindrical container by a piston at a height of 1 meter. The pressure outside the container is 100 kPa. The pressure inside the container is initially 1000 kPa. The gas expands rapidly at constant temperature, pushing the piston upward. At what height does the piston come to rest? What is the work done by the gas in this expansion? (10 points) The piston comes to rest when P 2 = P ext = 100kPa P 1 V 1 = P 2 V 2 (1000kPa)( π r 2 )(1m) = (100kPa)( π r 2 )(h) h = 10m ) V )(V P ( dV P W 1 2 ext ext = = W = (-10 5 Pa)[ π (1m) 2 (10m – 1m)] W = -2827 kJ The gas does 2827 kJ of work 2
ChBE 321 – Chemical Engineering Thermodynamics Exam #1 – February 15th, 2008 (b) At the bottom of the container is a 2-cm-diameter hole which has been plugged. The plug is removed, and the piston falls at a rate of 1cm/s. What is the exit velocity of the gas at the hole? Assume that gas density is constant and steady state process (10 Points) ρ 1 u 1 A 1 = ρ 2 u 2 A 2 ( ρ )(1cm/s)[ π (100cm) 2 ] = ( ρ )(u 2 )[ π (1cm) 2 ] u 2 = 100m/s 3

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Exam%201_Solutions - ChBE 321 Chemical Engineering...

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