HW3-336 - ME 336 PROBLEM SET 3 8.5 Water at 100 C, quality...

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ME 336 PROBLEM SET 3 8.5 Water at 100 o C, quality 50% in a rigid box is heated to 110 o C. How do the properties (P, v, x, u and s) change? (increase, stay about the same, or decrease) A fixed mass in a rigid box give a constant v process. So P goes up (in the two-phase region P = P sat at given T) v stays constant. x goes up ( we get closer to the saturated vapor state see P-v diagram) u goes up (Q in and no work) s goes up (Q in) 8.27 Find the entropy for the following water states and indicate each state on a T-s diagram relative to the two-phase region. a. 250 o C, v = 0.02 m 3 /kg b. 250 o C, 2000 kPa c. –2 o C, 100 kPa Solution: a) Table B.1.1: 0.001251 = v f < v < v g = 0.05013 m 3 /kg => Two-phase x = 0.02 - 0.001251 0.04887 = 0.38365 s = s f + x s fg = 2.7927 + 0.38365 3.2802 = 4.05 kJ/kg K b) Table B.1.1: P < P sat = 3973 kPa => superheated vapor B.1.3 s = 6.5452 kJ/kg K c) Table B.1.1 T < T tripple =0.01 o C so goto B.1.5 Table B.1.5: P > P sat = 0.5177 kPa so compressed solid s = –1.2369 kJ/kg K P v 1 2 T s 1 2
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P s T a b c a b c 8.49 A cylinder fitted with a piston contains ammonia at 50 C, 20% quality with a volume of 1 L. The ammonia expands slowly, and during this process heat is transferred to maintain a constant temperature. The process continues until all the liquid is gone. Determine the work and heat transfer for this process. Solution: C.V. Ammonia in the cylinder. 1 2 T s 50 C NH 3 o Table B.2.1: T 1 = 50°C, x 1 = 0.20, V 1 = 1 L v 1 = 0.001777 + 0.2 0.06159 = 0.014095 m 3 /kg s 1 = 1.5121 + 0.2 3.2493 = 2.1620 kJ/kg K m = V 1 /v 1 = 0.001/0.014095 = 0.071 kg v 2 = v g = 0.06336 m 3 /kg, s 2 = s g = 4.7613 kJ/kg K Process: T = constant to x 2 = 1.0, P = constant = 2.033 MPa From the constant pressure process 1 W 2 = PdV = Pm(v 2 - v 1 ) = 2033 0.071 (0.06336 - 0.014095) = 7.11 kJ From the second law Eq.8.3 with constant T 1 Q 2 = TdS = Tm(s 2 - s 1 ) = 323.2 0.071(4.7613 - 2.1620) = 59.65 kJ or 1 Q 2 = m(u 2 - u 1 ) + 1 W
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HW3-336 - ME 336 PROBLEM SET 3 8.5 Water at 100 C, quality...

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