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cheme141-Fall06-mt2-Chu-soln

cheme141-Fall06-mt2-Chu-soln - ChE 141 Midterm 2 Fall 2006...

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ChE 141 Midterm 2 Fall 2006 1) Note: For this problem the sign convention used is for quantities into a system are positive and quantities leaving the system are negative. a) (15 points) H 4 is given so H 1 can be found from adding the work for the pump or H 1 = H 4 +W 41 = 188.4 kJ/kg + 8.676 kJ/kg = 197.1 kJ/kg = H 1 (3 points) H 3 can be found on page 722 of your book (since it is saturated vapor). H 3 = 2584.8 kJ/kg (3 points) W 23 = H 3 – H 2 = 2584.8 kJ/kg – 3391.6 kJ/kg = -806.8 kJ/kg = W 23 (3 points) To find H 3 ’, we need to know the steam quality, x’. S 2 = S 3 ’ because we are looking at the isentropic case. S 2 = 6.6858 kJ/(kg*K) = S 3 satvap x’ + S 3 satliq (1-x’) (1 point) = 8.1511 kJ/(kg*K) * x’ + 0.6493 kJ/(kg*K) * (1-x’) x’ = 0.805 (1 point) Now, we can get H 3 ’. H 3 ’ = H satvap x’ + H satliq (1-x’) = 2584.8 kJ/kg * 0.804 + 191.832 kJ/kg * (1 – 0.804) H 3 ’ = 2117.8 kJ/kg (1 point) W 23 ’ = H 3 ’ – H 2 = 2115.8 kJ/kg – 3391.6 kJ/kg = -1275.8 kJ/kg = W 23 (3 points) b) (9 points) Q 12 = H 2 – H 1 = 3391.6 kJ/kg – 197.1 kJ/kg = 3194.5 kJ/kg = Q 12 (3 points) Q 34 = H 4 – H 3 = 188.4 kJ/kg – 2584.8 kJ/kg = -2396.4 kJ/kg = Q 34 (3 points) Q 34 ’ = H 4 - H 3 ’ = 188.4 kJ/kg – 2115.8 kJ/kg = -1927.4 kJ/kg = Q 34 (3 points)
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c) (10 points) turbine ! = 632 . 0 = ! ! = = = kg kJ kg kJ W W W W turbine turbine turbine / 6 . 1275 / 8 . 806 ' ' 23 23 " 0.632 = η turbine = + ! = + = = 5 . 3194 676 . 8 8 . 806 12 41 23 Q W W Q W H net cycle " 0.250 = η cycle For each efficiency: 2 points for correct fraction 3 points for final answer d) (10 points) Note: for this section a subscript S refers to the isentropic case to avoid any confusion. First, we need to realize what has been affected by the leak. Since the boiler has the leak, Q 12 and H 2 will be affected. Since H 2 will be different, W 23 and the isentropic work, W’ 23 , will also be affected. Using the conditions given for state 2’’, we can find H 2 ’’ on page 739 with some interpolation using the entries for 3400 kPa at 375°C and 350°C.
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