TH-008-Examples Chapter Eight PDF

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By M.Sc.: Hyder M. Abdul Hussein Thermodynamics – Chapter Eight - Entropy 7–24 A rigid tank contains an ideal gas at 40°C that is being stirred by a paddle wheel. The paddle wheel does 200 kJ of work on the ideal gas. It is observed that the temperature of the ideal gas remains constant during this ...

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By M.Sc.: Hyder M. Abdul Hussein Thermodynamics – Chapter Eight - Entropy

7–24 A rigid tank contains an ideal gas at 40°C that is being stirred by a paddle wheel. The paddle wheel does 200 kJ of work on the ideal gas. It is observed that the temperature of the ideal gas remains constant during this process as a result of heat transfer between the system and the surroundings at 30°C. Determine the entropy change of the ideal gas. ∆S = 0 S2 = S1

7–25 Air is compressed by a 12-kW compressor from P1 to P2. The air temperature is maintained constant at 25°C during this process as a result of heat transfer to the surrounding medium at 10°C. Determine the rate of entropy change of the air. State the assumptions made in solving this problem. Answer: - 0.0403 kW/K h = h(T) for ideal gases, we have h1 = h2 since T1 = T2 = 25°C. ̇ ̇ ̇

8.57 A closed tank, with V = 10 L, containing 5 kg of water initially at 25◦C is heated to 175◦C in a reversible process. Find the heat transfer to the water and its change in entropy.

C.V.: Water from state 1 to state 2. Energy Eq.: m (u2 − u1) = 1Q2 − 1W2 Entropy Eq.: m (s2 − s1) = ∫ dQ/T Process: constant volume (reversible isometric) so W1-2 = 0 State 1: v1 = V/m = 0.002 from steam table x1 = (0.002 - 0.001003)/43.358 = 0.000023 u1 = 104.86 + 0.000023 × 2304.9 = 104.93 kJ/kg s1 = 0.3673 + 0.000023 × 8.1905 = 0.36759 kJ/kg K

Continuity eq. (same mass) and V = C fixes v2 State 2: T2, v2 = v1 so from steam table B.1.1 x2 = (0.002 - 0.001121)/0.21568 = 0.004075 u2 = 740.16 + 0.004075 × 1840.03 = 747.67 kJ/kg s2 = 2.0909 + 0.004075 × 4.5347 = 2.1094 kJ/kg K Energy eq. has W = 0, thus provides heat transfer as Q1-2 = m (u2 - u1) = 3213.7 kJ The entropy change becomes m(s2 - s1) = 5(2.1094 – 0.36759) = 8.709 kJ/K 8.66 Water at 1000 kPa, 250°C is brought to saturated vapor in a piston/cylinder with an isobaric process. Find the specific work and heat transfer. Estimate the specific heat transfer from the area in the T-s diagram and compare it to the correct value.

Energy Eq.: u2 − u1 = q1-2 – w1-2 Entropy Eq.: s2 − s1 = ∫ dq/T Process: P = C » w = ∫ P dv = P(v2 − v1) 1: Steam table v1= 0.23268 m3/kg, s1= 6.9246 kJ/kgK, u1 = 2709.91 kJ/kg 2: Steam table v2 = 0.19444 m3/kg, s2 = 6.5864 kJ/kg K, u2 = 2583.64 kJ/kg, T2 = 179.91°C From the process equation w1-2 = P (v2 − v1) = 1000 (0.1944 – 0.23268) = -38.28 kJ/kg From the energy equation q1-2 = u2 − u1 + w1-2 = 2583.64 – 2709.91 – 38.28 = -164.55 kJ/kg Now estimate the heat transfer from the T-s diagram. 1q2 = ∫ T ds = AREA ≅ 12 (T1 + T2)(s2 − s1) = 12 (250 + 179.91 + 2 × 273.15)(6.5864 – 6.9246) = 488.105 × (-0.3382) = -165.1 kJ/kg Very close approximation. The P = C curve in the T-s diagram is nearly a straight line. Look at the constant P curves on Fig.E.1. Up over the critical point they curve significantly.

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7–32 A 0.5-m3 rigid tank contains water initially at 200 kPa and 40 percent quality. Heat is transferred now to the water from a source at 35°C until the pressure rises to 400 kPa. Determine (a) the entropy change of the water, (b) the entropy change of the heat source, and (c) the total entropy change for this process. Answers: (a) 3.880 kJ/K, (b) -3.439 kJ/K, (c) 0.441 kJ/K

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7–34 A well-insulated rigid tank contains 2 kg of a saturated liquid–vapor mixture of water at 100 kPa. Initially, three-quarters of the mass is in the liquid phase. An electric resistance heater placed in the tank is now turned on and kept on until all the liquid in the tank is vaporized. Determine the entropy change of the steam during this process. Answer: 8.10 kJ/K

7–46 A piston–cylinder device contains 1.2 kg of saturated water vapor at 200°C. Heat is now transferred to steam, and steam expands reversibly and isothermally to a final pressure of 800 kPa. Determine the heat transferred and the work done during this process.

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