Lab2

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Mechanical Engineering

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Dec 6, 2023

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First Law of Thermodynamics (Lab 2) 1. For this lab, you will use the PhET simulation: https://phet.colorado.edu/sims/html/gas-properties/latest/gas-properties_en.html and click on the “Ideal” tab. 2. Put in 500 heavy particles into the container, lower temperature to T = 255 K, and adjust width to w = 7.10 nm. Record 10 pressure value (in kPa) readings (every fourth push of “time increment” button), calculate average pressure P (use Excel), and then calculate volume ! (in nm 3 ) using ideal gas model equation. Finally, determine the hidden area of container A (in nm 2 ) by dividing ! by w . 3. Isothermal Expansion from A to B ( T A = T B = 255 K): Under “Hold Constant”, click on “Temperature (T)”. Any adjustment to gas will be made with isothermal conditions, i.e., constant temperature conditions. a. In the chart below record pressure P 0 and volume V 0 measurements in the first row which are the values determined in 2. Increase the width w by 0.5 nm, record new volume V 1 (use A above to calculate), and take average of 10 pressure readings for P 1 in next row. Repeat this step (0.5 nm width increases) until you have filled out chart (total of 7 measurements). Points Pressure (kPa) Volume (nm 3 ) A B b. On Excel, plot the points: V on horizontal axis (points V 0 , V 1 , …, V 6 ) and P on vertical axis (points P 0 , P 1 , …, P 6 ). Hold onto this plot for later additions.

c. Determine the area Ar under the curve by doing the trapezoidal rule (approximation to integral): "# = ∑ ! !"# "! ! # (∆!) $ %&' where ∆! = ! ' − ! ( Note that the units of the Ar are *+, × ./ ) . Convert this Ar value to units of joules (J). The negative of Ar equals to the work ( 0 *+ < 0) done by the gas in the expansion. d. Work done by isothermal expansion (or contraction) can also be found by equation: 0 = 123 ln 7 , ! , $ 8 where in this case ! % = ! ( and ! - = ! $ . Do this calculation. Is it close to value found in part c.? This value is more accurate than part c since trapezoidal rule is approximation. e. What is the heat (in J) of the process, i.e., < *+ ? 4. Adiabatic Expansion from B to C: Under “Hold Constant”, click on “Nothing”. a. In the chart below record pressure P 0 and volume V 0 measurements in the first row coming from last row of table in 3. Note that temperature at point B , T B = 255 K. Increase volume by increasing width w by 0.5 nm increments until column of volume is filled ( V 1 , V 2 , …, V 6 ). b. Calculate the remaining pressure values ( P 1 , P 2 , …, P 6 ) using the adiabatic equation = % ! % . = = - ! - . where γ = / 0 and place in table below. c. Calculate the remaining temperature values ( T 1 , T 2 , …, T 6 ) using the adiabatic equation 3 % ! % .1' = 3 - ! - .1' where γ = / 0 and place in table below.

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Points Pressure (kPa) Volume (nm 3 ) Temperature (K) B C d. On Excel, add the additional 6 points on the plot from 3a: V on horizontal axis (points V 1 , V 2 , …, V 6 ) and P on vertical axis (points P 1 , P 2 , …, P 6 ). Hold onto this plot for later additions. e. Determine the area Ar under the curve by doing the trapezoidal rule (approximation to integral): "# = ∑ ! !"# "! ! # (∆!) $ %&' where ∆! = ! ' − ! ( Note that the units of the Ar are *+, × ./ ) . Convert this Ar value to units of joules (J). The negative of Ar equals to the work ( 0 +2 < 0) done by the gas in the expansion. f. What is the heat (in J) of the process, i.e., < +2 ? g. Use the simulator to move to a system defined by point C conditions by adjusting width and temperature. 5. Isobaric Compression from C to D: Under “Hold Constant”, click on “Pressure ‡T”. This will allow you to adjust volume of gas while holding pressure constant. a. Move width on simulator all the way back to w = 7.10 nm. What is the temperature reading T D ? b. What is the heat and work (in J) done in this process? Use equations < 23 = 1 / # 2∆3 and 0 23 = −=∆!.

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c. On Excel, add the additional 1 point on the plot of 4d.: P D , V D . 6. Isovolumetric Heating from D to E: Under “Hold Constant”, click on “Volume (V)”. This will allow you to adjust temperature of gas while holding volume constant. a. On simulator, heat up system back to first temperature T = 255 K. Pressure should be approximately back to where you started at point A. b. What is the heat and work (in J) done in this process, i.e., < 34 = 1 0 # 2∆3 and 0 34 , respectively? 7. Based all of the previous calculations, fill in the chart below: Process Change in Internal Energy ∆ E int (J) Heat Q (J) Work W (J) A to B (isothermal) B to C (adiabatic) C to D (isobaric) D to E (isovolumetric) 8. The total change in internal energy from A to E (add up second column above) is J . Is it close to 0? Which calculation could be introducing some error? 9. Attach Pressure vs. Volume Plot created in Excel from parts 3b., 4d., and 5c to this worksheet.