MEEN 315 PRINCIPLES OF THERMODYNAMICS SPRING 2017 Homework Cover page Student Last Name Student First Name UIN Section circle one HW Date Submitted Solution 204 504 2 Grading Completion All problems attempted Quality Neatness clarity legible Accuracy Accuracy of selected problem s Cover page this page attached on the top and all pages stapled together Total 10 points Max Score 4 1 4 1 Your Score 4 1 4 1 10 10 This cover page should be completed and stapled to the top of your homework solution MEEN 315 PRINCIPLES OF THERMODYNAMICS SPRING 2017 Homework Assignment 2 Due Jan 31 2017 at the beginning of the class Problem 1 A box having a mass of 25 lbm is pulled horizontally across a rough surface by a cable such that the box experiences a constant acceleration of 8 ft s2 to the right At the same time friction exerts a force of 3 lbf to the left as shown in the diagram Assuming the box starts from rest determine a the amount of work performed by the action of the cable in lbf ft after the box has traveled 20 ft b the speed of the box when it has travelled 20 ft and c the change in kinetic energy of the box after it has traveled 20 ft lbf ft Hint you will need to use Newton s Second Law F ma and the relation Vfinal Vinitial at Acceleration 8 ft s2 Box 25 lbm Cable Friction Force 3 lbf Problem 2 A frictionless piston cylinder contains a substance initially having a pressure of 320 kPa and volume of 2 m3 The contents are heated causing the piston to rise Once the piston has risen to three times the initial height the piston encounters stops The heating process continues until the pressure inside the system is doubled Draw the entire process on a P V diagram pressure vs volume labeling the states 1 3 on the diagram and indicate the numerical values of pressure and volume corresponding to each state on the PV diagram Compute the boundary work W that occurred during the entire process from state 1 to state 3 in kJ be sure to indicate whether the work is in or out of the system Initial state 1 Piston hits stops 2 3h h P 320 kPa V 2 m3 Final state 3 MEEN 315 PRINCIPLES OF THERMODYNAMICS SPRING 2017 Problem 3 A newly constructed wind turbine has a blade diameter of 60 m It is installed in a field having steady wind speed of 8 m s 1 The density of air is 1 25 kg m 3 The efficiency of the wind turbine is estimated to be 32 Calculate the total electric power generated by this wind turbine If the selling price of electricity is 0 95 kWh how much revenue does this wind turbine generate in one year Problem 4 A piston cylinder assembly is filled with a gas which undergoes a process during which the pressure specific volume relation is pv1 2 constant The mass of the gas is 1 lb and the initial pressure p1 160 lbf in2 initial volume V1 1 ft3 At the end of the process the final pressure p2 390 lbf in2 Also during this process heat transfer from the gas to the surrounding is 2 1 Btu You may assume kinetic and potential energy effects are negligible Determine the change in specific internal energy of the gas in Btu lb Problem 5 A typical air conditioning unit installed in a house has a coefficient of performance of 3 5 This unit is capable of providing 3000 Btu h of cooling while in operation In a particular year the A C unit operated for 125 days at 8 hours per day If the occupants had to pay 11 cents per kW h for electricity determine the cost for cooling in dollars for that year MEEN 315 PRINCIPLES OF THERMODYNAMICS Problem 1 Given 1 Mass of the box m 25lbm 2 Acceleration of the box a 8 ft s 2 3 Frictional force F f 3lbf 4 Distance traveled s 20 ft Find 1 Work done by the cable W 2 Speed of the box at s 3 Kinetic energy change Basic equations 1 F ma 2 v f vi at 3 W F L Solution a Since F ma lbf s 2 6 17lbf 32 4lbm ft Therefore Fp Ff 6 17lbf 9 17lbf As W Fp L 9 17lbf 20 ft 183 4lbf ft Fp Ff ma 25lbm 8 ft s 2 b Since V V0 at SPRING 2017 MEEN 315 PRINCIPLES OF THERMODYNAMICS SPRING 2017 t 1 Therefore L vdt v 0 t at 2 2 0 For v0 0 L 20ft 1 20 ft 8 ft s 2 t 2 2 t 2 24s v at 8 ft s 2 2 24s 17 92 ft s c 1 1 2 DEk m V 2 V0 2 25lbm 17 92 ft s 4014 08lbm ft 2 s 2 2 2 MEEN 315 PRINCIPLES OF THERMODYNAMICS SPRING 2017 Problem 2 Given 1 Pressure and specific volume at state 1 2 Path to reach state 2 3 3 Mass the substance 2kg Find 1 P V diagram 2 Total work done by the substance Assumption 1 The substance is an ideal gas 2 The specific volume of the substance is 2m3 kg Basic Equations 1 PV mRT 2 W F L Solution 1 point for accuracy Process 2 3 1 point for accuracy Process 1 2 a The work done by the substance during the whole process From 1 2 constant pressure W1 PDV 320 103 Pa 6 m3 2m3 1280 kJ b From 2 3 no work is done Therefore W W1 0 1280kJ out 1 point for accuracy MEEN 315 PRINCIPLES OF THERMODYNAMICS SPRING 2017 Problem 3 Given 1 Diameter of wind turbine D 60m 2 Velocity v 8m s and density r 1 25kg m3 3 Efficiency h 32 Find 1 Electric Power 2 Annual Revenue System Assumptions 1 No Temperature change before and after air comes in contact with the wind turbine 2 Pressure of the air stays the same 3 Velocity of air is in the direction normal to the plane containing the wind turbine Basic equations 1 DE DEK DE p DU Solution Since DE DEK DE p DU Also temperature pressure elevation change are negligible we have DE p 0 DU 0 Therefore DE DEK 1 mv22 mv12 2 For a single second 2 1 60 DE DEK 8m s p m 1 25kg m3 0 8m s 2 2 2 904 320 kg m2 s s2 kg m2 Nm J m Note F ma N kg Therefore W 2 2 s s s s s 904 320W Since h 32 P 32 904 320W 289 382 4W The revenue in an year at the rate of 0 95 kWhr 289 38kW 24hr day 365day yr 95 kWhr 2 408 220 36 yr MEEN 315 PRINCIPLES OF THERMODYNAMICS SPRING 2017 Problem 4 Known 1 A gas is compressed in a piston cylinder assembly 2 The pressure specific volume relation is specified Find …