3. (30 points) A gas contained in a piston-cylinder assembly undergoes three processes in series: Process...

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3. (30 points) A gas contained in a piston-cylinder assembly undergoes three processes in series: Process 12: Constant-volume process from state 1, where p = 1 bar and V = 6 m, to state 2, where p2 = 2 bar. Process 2 3: Compression to V3 = 2 m in which the pressure-volume relation is pV= constant. Process 34: Constant pressure to state 4, where V4 = 4 m. Sketch the processes on p-V coordinates and evaluate the work for each process in kJ. 4. (30 points) A gas is compressed in a piston-cylinder assembly from P = 200 kPa to P2 = 600 kPa and V = 0.02 m, in a process during which the relation between pressure and volume is PV 1.3= constant. The mass of the gas is 0.2 kg. If the specific internal energy of the gas increases by 100 kJ/kg during the process, determine the heat transfer, in kJ. Kinetic and potential energy changes are negligible. 5. (25 points) Four kilograms of nitrogen gas (N2) is in a rigid tank with a volume of 1 m. The tank is fitted with a paddle wheel that transfers energy to the gas by work at a constant rate of 12 W for 1 hour. In the process, the specific internal energy of the N2 increases by 10 kJ/kg. If no overall changes in kinetic and potential energy occur, determine a) The specific volume at the final state, in m/kg. b) The energy transfer by work, in kJ. c) The energy transfer by heat transfer, in kJ, and the direction of the heat transfer. Five problems, 100 points total. You must show schematics (except for question 1 and 2), and steps of your calculations to get full points. If you use data not given in the problem, give your source. Please follow the following problem-solving steps whenever applicable: Step 1: Problem Statement Step 2: Schematic Step 3: Engineer Model: Assumptions and Approximations Step 4: Physical Laws Step 5: Properties Step 6: Calculations Step 7: Reasoning, Verification, and Discussion Dimensions and Units 1. (10 points) A closed faucet is dripping at the rate of one drop per second. Assume each drop is 0.05mL. How many cubic meters of water will be lost from the leak this January? Based on the cost of water in Tempe, AZ (search for this and cite your source), how much will the leak add to January's water bill? 2. (5 points) An orifice meter is used to measure the flow rate of fluids through a pipe. The flow rate is related to the pressure drop by an equation of the form APge u = c where u is fluid velocity in m/s, AP is pressure drop in N/m p is density of the fluid in kg/m, ge kg.m gravitational conversion factor, What are the dimensions and units of c? 1st Law of Thermodynamics and evaluating work 3. (30 points) A gas contained in a piston-cylinder assembly undergoes three processes in series: Process 12: Constant-volume process from state 1, where p = 1 bar and V = 6 m, to state 2, where p2 = 2 bar. Process 2 3: Compression to V3 = 2 m in which the pressure-volume relation is pV= constant. Process 34: Constant pressure to state 4, where V4 = 4 m. Sketch the processes on p-V coordinates and evaluate the work for each process in kJ. 4. (30 points) A gas is compressed in a piston-cylinder assembly from P = 200 kPa to P2 = 600 kPa and V = 0.02 m, in a process during which the relation between pressure and volume is PV 1.3= constant. The mass of the gas is 0.2 kg. If the specific internal energy of the gas increases by 100 kJ/kg during the process, determine the heat transfer, in kJ. Kinetic and potential energy changes are negligible. 5. (25 points) Four kilograms of nitrogen gas (N2) is in a rigid tank with a volume of 1 m. The tank is fitted with a paddle wheel that transfers energy to the gas by work at a constant rate of 12 W for 1 hour. In the process, the specific internal energy of the N2 increases by 10 kJ/kg. If no overall changes in kinetic and potential energy occur, determine a) The specific volume at the final state, in m/kg. b) The energy transfer by work, in kJ. c) The energy transfer by heat transfer, in kJ, and the direction of the heat transfer. Five problems, 100 points total. You must show schematics (except for question 1 and 2), and steps of your calculations to get full points. If you use data not given in the problem, give your source. Please follow the following problem-solving steps whenever applicable: Step 1: Problem Statement Step 2: Schematic Step 3: Engineer Model: Assumptions and Approximations Step 4: Physical Laws Step 5: Properties Step 6: Calculations Step 7: Reasoning, Verification, and Discussion Dimensions and Units 1. (10 points) A closed faucet is dripping at the rate of one drop per second. Assume each drop is 0.05mL. How many cubic meters of water will be lost from the leak this January? Based on the cost of water in Tempe, AZ (search for this and cite your source), how much will the leak add to January's water bill? 2. (5 points) An orifice meter is used to measure the flow rate of fluids through a pipe. The flow rate is related to the pressure drop by an equation of the form APge u = c where u is fluid velocity in m/s, AP is pressure drop in N/m p is density of the fluid in kg/m, ge kg.m gravitational conversion factor, What are the dimensions and units of c? 1st Law of Thermodynamics and evaluating work