Adiabatic Compression: Sensor Calibration, Work, and the Adiabatic Index γ (Revised instructions, PS253, Summer A 2016)

You will follow the procedure outlined in the next document, with these modifications to the instructions:

1. For the experimental procedure, described in steps 16-21, repeat the procedure so that you have data for 5 separate compression runs. (Make sure you allow the device to cool back to equilibrium with the room between runs.)

2. Your report does not need to be a full article with abstract, intro, conclusion, etc. Instead, you will focus on the theory and the analysis that you make on your data based on the theory.

a) Theory: On page 3, there is a section on the theory of work done during the compression of the gas. Make sure you understand, and describe how equation 11 is converted to equation 12, and how the Riemann sum of all the terms of equation 13 from your data represents the same work as equation 12.

b) Analysis: You will submit a MSExcel file with the Riemann sum giving the work done for each of your runs. Make sure the file is organized and labeled so that the instructor can see your work is done correctly. Make sure unit conversions are done correctly. Your report should have a table with the results of work done, calculated using this method, for each of the 5 runs. The results should be very similar for each run. Include each individual run's percent difference from the mean of the 5 runs in your table.

c) Theory: Understand and explain the theoretical analysis done on pages 1-3, starting with the first law of thermodynamics and yielding the two Ln vs Ln equations containing γ in the slopes (equations 8 and 9).

d) Analysis: Using the Ln vs Ln plots from your data, identify the 10 different experimental γ's. (Important: You must use only data points representing the adiabatic compression segments of you runs for this analysis to work---explain this in your report, and make sure these subsets of your data are clearly identified in your MSExcel submission.) The experimental γ's should be presented in a table in your report.

e) Analysis: Use the theoretical work equation (equation 15) for each of your 5 runs, using each of the three possible candidates for γ (your 2 experimental γ's, and a reference version for air). Next compare each of the three "theoretical work" results with your Riemann sum "experimental work" for each run. Present these results and comparisons in a table for your report. Which γ seems to best represent the air in the lab?

3. Your final deliverables for the lab should be a pdf of your partial report (theory section and presentation of results), and an xls or other Excel file clearly presenting your data and the analysis done on it.

In the adiabatic compression experiment, we first had to use the machine in (figure 1). However, in order to use the machine we had to calibrate all the sensors. The sensors were to measure pressure, volume, and temperature. By the time we finished calibrating the sensors, these initial result were calculated (Table 1).

Table 1

dU=dQ-dW (1)

"Where dU is change in the internal energy, dQ is the sum of the heat added or subtracted, and dWis the work done on or by the system. Note that in this case the number of particles inside the system must remain constant; if the particle count changed an extra term dn would need to be included. Solving Eq. 1 for the change in heat and applying it to a system in adiabatic conditions (dQ=0) we obtain." according the guideline (Adiabatic Compression, page 1)

dQ = dU+dW=0 (1)

dW = PdV (3)

dU = C_vdT (4)

PdV +VdP=d(PV)=nRdT (5)

ln? P = -γ ln?V + C' (6)

Where P is pressure in the system, V is volume of the system, γ is the adiabatic index, and C' is an integrating constant. It is noticeable that Eq.6 is in the form of a linear equation.

ln? T = - (γ-1) ln?V + C' (7)

The total work done in adiabatic compression can be expressed equation (8). Where W_theor is the theoretical work done in the adiabatic compression.

W_theor = P₁V₁^γ ((V_n^(1-γ) - V₁^(1-γ)))/(1-γ)

Calculation: We did the experiment five times to create a graph.

dU = dQ-dW (1)

"Where dU is change in the internal energy, dQ is the sum of the heat added or subtracted, and dWis the work done on or by the system. Note that in this case the number of particles inside the system must remain constant; if the particle count changed an extra term dn would need to be included. Solving Eq. 1 for the change in heat and applying it to a system in adiabatic conditions (dQ=0) we obtain." according the guideline (Adiabatic Compression, page 1)

dQ = dU + dW = 0 (1)

dW = PdV (3)

dU = C_vdT (4)

PdV +VdP = d(PV) = nRdT (5)

ln? [ P = -γ ln?V + C''  (6)

Where P is pressure in the system, V is volume of the system, γ is the adiabatic index, and C' is an integrating constant. It is noticeable that Eq.6 is in the form of a linear equation.

ln? [ T = - (y - 1) ln?V + C'' (7)

The total work done in adiabatic compression can be expressed equation (8). Where W_theor is the theoretical work done in the adiabatic compression.

W_theor = P₁V₁-^(γ-1) - ln?V₁^1-y]/1 - y (8)

Calculation: We did the experiment five times to create a graph.

Attachment:- adiabatic final.rar