thermodynamics hw 2 (1) (1)

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student name : Shyanne Smith Date : 09/08/2023 All work shown on pictures of paper at the end of this word document Homework Assignment No.2 I. Indicate whether the following statements are true or false 1. In local surroundings at standard atmospheric pressure, a gage will indicate a pressure of 0.2 atm for a refrigerant whose absolute pressure is 1.2 atm. A: True 2. Volume is an extensive property. A: True 3. The pound force, lbf, is equal to the pound mass, lb. B: False Lbf is the force acting upon the mass, a bathroom scale is an example, pound mass is the actual mass of the object 4. A control volume is a special type of closed system that does not interact in any way with its surroundings. B: False A control volume is an open system meaning the system interacts with its surroundings. 5. A spring is compressed adiabatically. Its internal energy increases. A: True\ True because an adiabatical process has no heat transfer into or out of the system. The potential energy within the spring is increased when compressed, which is its internal energy.

6. If a system’s temperature increases, it must have experienced heat transfer. B: False Adiabatic system is an example, work done on the system increases the internal energy which increases temperature. 7. For power cycle efficiency is always lower than 100 %. A: True Friction and heat loss account for the efficiency being less than 100%. There is never a 100% efficient heat cycle. 8. For heat pumps, the coefficient of performance y is always greater than or equal to one. A: True 9. For any cycle, the net amounts of energy transfer by heat and work are equal. B: False Only isothermal processes. 10. If a closed system undergoes a thermodynamic cycle, there can be no net work or heat transfer. A: True From first law of thermodynamics II. Checking understanding 1. The symbol D is always used to denote C: final value minus initial value 2. What is being transferred to the system if we heat it up? A: Energy

3. The resultant pressure force acting on a body completely or partially submerged in a liquid is the buoyant force 4. The differential of work, δ W, is said to be an _inexact_ differential. B. Inexact 5. What direction is the net energy transfer by work for a refrigeration or heat pump cycle: in or out? A: In 6. What direction is the net energy transfer by heat for a refrigeration or heat pump cycle: in or out? B: Out III. Perform the following unit conversions (tolerance ±2% approximately): (a) 1.1 L to in. 3 Answer: 67.1 in^3 (b) 715.0 J to Btu Answer: 0.678Btu

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(c) 0.1485 kW to ft·lbf/s Answer: 109.5ft*lbf/s (d) 415.8 g/s to lb/min Answer: 55lb/min IV. Air contained within a piston–cylinder assembly is slowly compressed. As shown in picture below, during this process the pressure first varies linearly with volume and then remains constant. Determine the total work, in kJ. Solution

KNOWN : The graph shows air in a piston-cylinder assembly being slowly compressed. Pressure varies linearly with volume at first, but then remains constant. FIND : We need to find the total work in kJ units. SCHEMATIC AND GIVEN DATA : y-axis is pressure and x-axis is volume both in SI units which is good because our answer will be in SI units. P1= 100kPa P2=150kPa V1=0.07m^3 V2=0.055m^3 V3= 0.015m^3 ENGINEERING MODEL : Need to find the area under the curve for the total work done. First the area from point 1-2 then from 2-3.

ANALYSIS : Work is shown on pictures of paper, but essentially I found that if you draw a trapezoid and rectangle with the area under the curve and then add them together, it gives you the total area. We could also integrate the area under the curve and that would’ve given the same result. The total work done is W=-7.875kJ IV. A system undergoing a power cycle develops a steady power output of 0.3 kW while receiving energy input by heat transfer at a rate of 2400 Btu/h. Determine the thermal efficiency and the total amount of energy developed by work, kW ⋅ h, for 1 full year of operation. KNOWN : We are given the work output of W=0.3kW which is hourly. We know the heat transfer rate is 2400Btu/hour so that is an hourly rate. FIND : We want to know the thermal efficiency which is a percentage and the amount of energy (work) outputted in one year. SCHEMATIC AND GIVEN DATA : Thermal efficiency= n=W/Q which is work dividded by heat energy input Heat energy input=Q=2400Btu/h

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Power output=W=0.3kW ENGINEERING MODEL : We have the values we need to put into the equations. The only conversion we need to do is Btu to kW. ANALYSIS : Work done on paper. Efficiency= 43% and 1 year work is 2,628kW VI. A gas in a piston–cylinder assembly undergoes a process for which the relationship between pressure and volume is pV 2 = constant . The initial pressure is 1 bar, the initial volume is 0.1 m3, and the final pressure is 9 bar. Determine (a) the final volume, in m3, and (b) the work for the process, in kJ KNOWN : We know: P1=1bar P2=9bar and V1=0.1m^3 PV^2 = constant where n=2 since the standard is PV^n=constant FIND : We need to find V2 and the work done for the process SCHEMATIC AND GIVEN DATA : Work= W= P1V1-P2V2/n-1 where n=2 P1V1^2=P2V2^2 V2= sqrt(P1V1^2/P2)

ENGINEERING MODEL : Plug and chug values into equations (basic math) ANALYSIS : Work done on paper V2= 0.03333m^3 Work=W=-20kJ

VII. A coefficient of performance of a refrigeration cycle operating as shown in the figure below is β = 1.8. For the cycle, Q out = 250 kJ. Determine Q in and W cycle, each in kJ. (HINT: Check units, sign and equations. Refer to Sections 2.6.1 and 2.6.3). . Solution KNOWN : β = 1.8. For the cycle, Q out = 250 kJ. FIND : We need to find Qin and Work done on the cycle. SCHEMATIC AND GIVEN DATA : We are given values that plug directly into equations

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