ME495 Lab 10_ Ratio of Volumes

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Apr 3, 2024

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Ratio of Volumes ME 495: Mechanical and Thermal Systems Lab Section 05: Thursday Group D Authors: Soeung Khanitha, Smith Emilee, Sichantha Jack, Taylor Charles Instructor: Dr. Hamid Nourollahi Wednesday, March 13, 2024

1 Table of Contents Objective of Experiment (Khanitha Soeung) ................................................................................... 2 List of Symbols and Equations (Charles Taylor) ............................................................................. 2 Equipment (Khanitha Soeung & Jack Sichantha) ............................................................................ 3 Experimental Setup (Khanitha Soeung, Jack Sichantha) ................................................................. 4 Experimental Procedure (Emilee Smith) ......................................................................................... 6 Experimental Results(Charles Taylor) .................................................................................... 8 Discussion of Results (Charles Taylor) ............................................................................................ 9 Lab Guide Questions (Emilee Smith) ............................................................................................ 10 Conclusion (Jack Sichantha) .......................................................................................................... 11 References ( Khanitha Soeung ) .................................................................................................... 12 Appendix (Khanitha Soeung) ........................................................................................................ 12 List of Figures Figure 1: Illustrates the TH5 apparatus for expansion processes of a perfect gas, developed by Armfield Limited .................................................................................................................. 4 Figure 2: Electrical Console; (A) Front Perspective, (B) Rear Perspective…………………..5 Figure 3: Equipment Diagrams …………………………………………………………….6 List of Tables Table 2: Figure 2 Equipment Diagram reference from lab manual ..................................... 7 Table 2: Experimental Data Two pressure sensors are employed, both utilizing piezoresistive technology, generating a voltage output that varies linearly with pressure fluctuations from lab manual ............................................................................................... 8 Table 3: Pressure Sensors ................................................................................................... 8

2 Objective of Experiment (Khanitha Soeung) The objective of this experiment is to determine the ratio of volumes for air in two vessels through an isothermal expansion process, providing students with practical insight into ideal gas behavior, adiabatic processes, and thermodynamics' first law. Utilizing the TH5-B equipment, which introduces basic thermodynamic processes using air as a working fluid, the setup comprises interconnected rigid vessels—one for pressurized operation and the other for vacuum operation—allowing for independent or combined evaluation of thermodynamic processes. Constructed from clear rigid plastic, the vessels maintain moderate insulation to minimize external temperature influences while permitting rapid return to ambient temperature. The teams hypothesize that the volume ratio of air in the vessels will remain constant throughout the expansion, in accordance with Boyle's Law and ideal gas principles. The team also hypothesized that, when calculating the ratio of volumes, error should be less than 10%. List of Symbols and Equations (Charles Taylor) Table 1: Symbols and Equations PARAMETER SYMBOL / EQUATION UNIT Constant Temperature for both vessels T °C Atmospheric Pressure P atm 101325 N/m 2 Initial Pressure for first vessel (Measured) P s N/m 2 Initial Pressure for first vessel (Absolute) P1abs s = P atm + P s N/m 2 Initial Vacuum for second vessel (Measured) V s N/m 2 Initial Pressure for second vessel (Absolute) P2abs s = P atm - V s N/m 2 Final pressure (Measured) P f = -V f N/m 2 Final Pressure (Absolute) P1abs f = P f + P atm N/m 2 Ratio of Volumes R=Vol1/Vol2 𝑉𝑜𝑙1/𝑉𝑜𝑙2 = (𝑃2???, ? − 𝑃𝑓)/(𝑃𝑓 − 𝑃1???, ?) Ratio of Volumes From Data Logger Ro Percent Error 𝐸??𝑜? = |𝑅 − 𝑅𝑜|/𝑅 %

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3 Note: A majority of this table is directly cited from the lab guide manual This is given in the references of this report as reference number [1] Equipment (Khanitha Soeung & Jack Sichantha) ● Temperature Probes (T1 & T2) ○ Miniature semiconductor thermistor beads with fine connecting leads, installed between support wires at the tip of the probe assembly; exhibit nonlinear negative resistance characteristics; fast response to temperature changes. ● Air Pump ○ Supplies air for evaluating thermodynamic properties of a perfect gas; inlet connected to tapping on top of evacuated vessel, outlet connected to tapping on top of pressurized vessel. ● Electrical Console ○ Simple console with power supplies and necessary connections for air pump and sensors; displays pressure (P), vacuum (V), and temperatures (T1 & T2) on a digital meter with rotator selector switch. ● IFD5 ○ Interface device allowing voltage signals from measurements to be connected to a PC; connects to console via 50-way data cable and to PC via USB cable; features red 'Power' LED indicating connection to PC and green 'Active' LED indicating recognition by PC.

4 Experimental Setup (Khanitha Soeung, Jack Sichantha)

5 Figure 1: Illustrates the TH5 apparatus for expansion processes of a perfect gas, developed by Armfield Limited. Figure 2: Electrical Console; (A) Front Perspective, (B) Rear Perspective The setup procedure began with ensuring that the Mains on/off switch on the electrical console was in the OFF position, along with the air pump switch. Ball valves V1, V2, and V3 on top of the vessels were fully opened, and isolating valves V4 and V7 from the air pump to the pressurized and evacuated vessels were also opened entirely. Following this, the inlet of the air pump was connected to the tapping on top of the evacuated vessel, while the outlet was connected to the tapping on the top of the pressurized vessel. Leads from the sensors were connected to the appropriate sockets at the rear of the electrical console. After ensuring the mains electrical supply was connected and switched on, the operation of the RCD was tested, and the miniature circuit breakers were confirmed to be in the ON position. The mains on/off switch on the front of the electrical console was set to the ON position, and the digital panel meter was observed to be illuminated. The rotary selector switch was set to each position in turn to check

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6 the readings. Ball valves V1 and V2, along with isolating valve V6, were closed, and isolating valve V4 was opened to allow the air pump to pressurize the pressurized vessel. The selector switch was set to position P to observe the pressure inside the pressurized vessel, and the air pump was switched ON. Once the pressure reached approximately 30 kN/m2, isolating valve V4 was closed, and the air pump was switched OFF. Similar procedures were followed for observing the vacuum inside the evacuated vessel. Finally, valves V1, V2, and V3 were opened to return the vessels to atmospheric pressure, and the equipment was switched OFF using the mains switch on the electrical console. Experimental Procedure (Emilee Smith) Figure 3: Equipment Diagrams Before commencing the exercise, it was ensured that both rigid vessels were at atmospheric pressure by opening valves V1 and V3 on top of the vessels and closing all other valves. The atmospheric pressure (Patm) was assumed to be 760 mm of Hg (or 10130 N/m2). Ball-valves V1, V3, and V5 were closed, while V4 and V7 were opened. The large vessel was pressurized by switching ON the air pump, and when the pressure (P) reached approximately 30 kN/m2, the air pump was switched OFF, and valves V4 and V7 were closed. After allowing the

7 pressure in the large vessel to stabilize, the starting pressure (Ps) and ambient temperature (Ts) were recorded. The software was configured to take samples at 1-second intervals, and data logging was initiated by pressing the green 'Go' button. Needle valve V5 was fully closed, and isolating valve V6 was opened, with V5 opened slightly to allow air to leak from the pressurized vessel to the evacuated vessel. V5 was adjusted to ensure a slow decrease in P without any change in T1 or T2. Once the vessel contents stabilized in pressure and temperature, the final pressure (Pf) was recorded. Data logging was stopped by pressing the red 'Stop' button, and the data for each trial was saved as an Excel file on a portable USB drive. Table 2: Figure 2 Equipment Diagram reference from lab manual

8 Table 2: Experimental Data Two pressure sensors are employed, both utilizing piezoresistive technology, generating a voltage output that varies linearly with pressure fluctuations from lab manual Table 3: Pressure Sensors Experimental Results (Charles Taylor) Table 4: Experimental Pressure Values Trial Initial Pressure Final Pressure Ps (kN/m^s) P1abss (kN/m^s) Vs (kN/m^s) P2abss (kN/m^s) Pf (kN/m^s) P1absf (kN/m^s) 1 34.46 134.46 34.46 65.54 114.48 14.48 2 34.46 134.46 34.46 65.54 112.96 12.96 3 34.46 134.46 34.46 65.54 112.56 12.56 4 34.46 134.46 34.46 65.54 114.29 14.29 5 34.46 134.46 34.46 65.54 114.82 14.82 Table 5: Experimental R Values and Error R Ro (From Data Logger) Error (%) 2.449 2.36 3.651 2.205 2.15 2.520 2.147 2.12 1.259 2.416 2.36 2.356 2.509 2.41 3.952

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9 Sample Calculations: Trial 1 First, initial pressures are recorded and noted. These are all found in table 4. Now calculate Pf: Pf = -Vf + Patm, Vf is recorded to be -14.48 kN/m^2. Hence, Pf = 114.48 kN/m^2 Now calculate P1abs,f: P1abs,f = Pf - Patm, Pf = 114.48 kN/m^2. Hence, P1abs,f = 14.48 kN/m^2 Now calculate R: , P2abs,s, Pf, and P1 abs,s are found above 𝑅 = 𝑉𝑜𝑙1/𝑉𝑜𝑙2 = (𝑃2???, ? − 𝑃𝑓)/(𝑃𝑓 − 𝑃1???, ?) in table 4. R = 2.449 Now calculate Error: , R and Ro are found in table 4, Error = 3.952% 𝐸??𝑜? = |𝑅 − 𝑅𝑜|/𝑅 Discussion of Results (Charles Taylor) Table 4: Experimental Pressure Values represent the comparison of the data points for all the pressure found experimentally throughout the experiment. All initial pressures are taken directly from the data logger trials. The Ps represents the initial pressure for the first vessel, and P1abs,s is the absolute pressure for the first vessel. Vs and P2abs,s represent the initial pressures and vacuums for the second vessel. Pf was a calculated value using Vf and P1abs, and f is the absolute final pressure which is calculated using Pf and Patm. Table 5: Experimental R-Value and Error shows the experimental and theoretical values for R, Ro. R is calculated using the ratio of the volumes of the two containers, this equation can be shown in the lab guide. It is then compared to the Ro value shown in the data logger. This table also shows the error between these

10 two values. It is important to note that the calculated R-value is generally greater than its Ro counterpart. This shows that the error is likely a result of systematic error rather than random error, however, small random errors are likely still present. For example, a few systematic errors are the calibration of the machine or the wear of the pressure sensor. Random error should be uncommon in this experiment since the computer logs a majority of the data, however, turning the valve open too fast may cause excess pressure loss and could alter the data for each trial. The team’s hypothesis was that, when measuring the ratio volumes, the error found should be less than 10%. This turned out to be true in all cases and all trials. The error shown in table 4 proves that it was consistently less than 10% and even less than 4% in all cases. Lab Guide Questions (Emilee Smith) 1. Why is this an isothermal process? a. An isothermal process occurs when the temperature of a system remains constant. The temperature of this system remained roughly the same, fluctuating by tenths of a degree Celcius with a maximum temperature difference of 2.4°C in Trial 2. 2. How well does the result obtained compare to the expected result? Give possible reasons for any difference. a. The results from the experiment compared to the expected results were relatively close with a maximum percent error of 7.05% and a minimum percent error of 0.13%. Human error would be the most likely cause for any type of error because manually turning the knob will never be at the same rate each time and would also

11 change depending on the person turning it. Other reasons may involve any gas escaping from the vessels via worn seals/valves/etc. 3. Comment on the effect if the rate of change of pressure was sufficient to affect the temperature of the air inside the vessels. a. There was no effect from the rate of change of the pressure on the temperature of the air inside the vessels, which was expected since the experiment is an isothermal process. Conclusion (Jack Sichantha) Based on the data presented in Tables 3 and 4, it can be concluded that the experimental method employed to measure pressure and calculate the ratio of volumes between the two containers was effective and reliable. The systematic error observed, likely stemming from factors such as machine calibration and pressure sensor wear, was consistently small and below the threshold of 10% as hypothesized by the team. The low percentage of error, often less than 4%, indicates a high degree of precision in the experimental measurements. Furthermore, the rarity of random errors, attributed to the automated data logging process, underscores the robustness of the experimental setup. Nevertheless, precautions were taken to mitigate potential sources of random error, such as controlled valve operation. Overall, these findings validate the team's hypothesis and affirm the accuracy of the experimental procedure in determining the ratio of volumes between the containers. This not only contributes to the understanding of the physical properties under investigation but also highlights the importance of meticulous experimental design and execution in scientific research.

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12 References ( Khanitha Soeung ) [1] Nourollahi, A. (2024). ME-495 Laboratory Exercise – Number 10 – Ratio of Volumes In ME Dept, SDSU – Nourollahi. SDSU Publishing [2] Nourollahi, A. (2024). ME-495 Course Introduction_and Syllabus Spring 2024-1. In ME Dept, SDSU – Nourollahi. SDSU Publishing Appendix (Khanitha Soeung) The correlation between resistance and temperature for thermistors employed in TH5-B (Nominal Values) is as follows: