3. A completely reversible heat pump produces heat at a rate of 300 kW to warm a house maintained at 25°C. The exterior air, which is at 9°C, serves as the source. Calculate the rate of entropy change of the two reservoirs and determine if this heat pump satisfies the second law of thermodynamics, according to the increase of entropy principle. [MO7]

5. A power cycle operating between two thermal reservoirs receives energy QH by heat transfer from a hot reservoir at TH = 2000K and rejects Qc by heat transfer to a cold reservoir at Tc = 400K. For each of the following cases, determine whether the cycle operates reversibly, operates irreversibly, or is impossible. [MO1, MO5, MO6] a. QH b. QH c. QH = 1000kJ, Wycle = 850kJ 1000kJ, E = 60% 1000kJ, Qr= 200kJ

6. An engineer proposes to develop a power plant (which can be modeled as a heat engine) that will operate at an efficiency of 70%. The steam flowing through the power plant reaches a peak temperature of 750°F and rejects heat to the environment at a temperature of 70°F. Is this proposed power plant feasible, or does it violate the second law of thermodynamics? [MO1, MO3, MO5]

•The specific enthalpy of steam enters and leaves a steam turbine are 2915kJ/kg and 2355kJ/kg. Heat loss of the turbine is about 8kJ/kg. Kinetic energy and potential energy can be neglected. Find the work done by 1 kg of steam. •A heat exchanger works at 1 atm pressure and power of 2.0×106W, temperature of cold water enters the heat exchanger is 15°C as secondary side coolant. Find the minimum flow rate of coolant if the maximum outlet temperature is limited to 25°C.

1. A 75 wt. % solution of H₂SO4 is diluted using pure water to form a 25 wt. % solution of H₂SO4 (product). i) Calculate the mass of each inlet component required to make 1 kg of product. ii) If the pure water is at 37°C and the 75 wt. % H₂SO4 is at 0°C (inlet conditions), what is the temperature of the exit (product) stream if the process is conducted in an insulated tank? (Data can be obtained from the sulfuric acid mixing graph (Figure 8.1-1). [9] 2. Water (1) and H₂SO4 (2) are mixed at 21°C. The change in enthalpy of mixing is described by the following equation: AmixH=-74.4 x1 x2 (0.439 +0.561x₁) Given that the pure component enthalpies are: H₁ = 1.591 kJ/mol and H₂ = 1.596 kJ/mol i) Calculate the enthalpy of an equimolar mixture of water and sulfuric acid at this temperature. Use the equation provided. Compare your answer to that obtained from the sulfuric acid mixing graph (Figure 8.1-1). [10] ii) Calculate the heat evolved/absorbed during the process of mixing. [2]

1. Use the steam tables to evaluate the entropy departure function for steam at 25 MPa and 850°C.

3. (a) Use the steam tables to determine the fugacity of steam at 1.0 MPa and 850°C. (b) Calculate the fugacity if the pressure is increased to 100 MPa.

7. A fixed-volume container at 45°C contains 5 mol hexane liquid and 0.1 mol hexane vapor in equilibrium. An additional 0.2 mol of hexane vapor are added, while keeping the temperature constant. What happens to the pressure and the amount of liquid and vapor in the container? Why?

4. Diamond is denser than graphite. Sketch the chemical potentials of graphite and diamond as a function of pressure for a region over which a phase transition occurs. Explain the graph.

6. Water was subcooled to -37°C and then allowed to equilibrate adiabatically. Specify the final state of the system including temperature and amounts of each phase if more than one is present.

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