1. ENTC 370PROF. ALVARADO1 THERMODYNAMICS LAB Mass and Energy Analysis of Control Volumes Polytropic Processes ENTC - 370

2. 2 Polytropic Process(1) During expansion and compression processes of gases, the following relationship holds: The coefficient n depends on the process.

3. 3 Polytropic Process(2) During expansion and compression processes of gases, the following relationship holds: The coefficient n depends on the process.

4. ENTC 370PROF. ALVARADO4 Polytropic Process The coefficient n depends on the process: ― n=0, Isobaric process (constant pressure) 5-1 in graph. ― n=∞, Isometric process (constant volume) 2-6 in graph. ― n=1, Isothermal process (constant temperature) 4-8 in graph. ― n=k, Adiabatic process (no heat transfer) 3-7 in the graph. k=c p /c v =1.4 for air. Graph from www.taftan.com

5. ENTC 370PROF. ALVARADO5 Polytropic Process Boundary work:

6. -Pressurized air inside a pressure vessel is expanded in a polytropic process using three discharge valves with small, medium and large orifices. The measured temperature and pressure for the process are posted. 1.Use the ideal gas law, Pv = RT, to compute v for each corresponding P. Use SI units: m3/kg for v, kPa for P and ºK for T. 2.Plot ln(P) versus ln(v) and find n: a.For each run, on a separate graph, plot ln(P) [on the ordinate (vertical) axis] versus ln(v) [on the abscissa (horizontal) axis]. b.Determine the polytropic exponent n by using a linear model of each run. Also find the correlation coefficient R 2. 3.Discuss the meaning of your n values, that is, how do the n values compare with n values for other, known processes (see previous slide)? ENTC 370PROF. ALVARADO6 Problem 1: Polytropic Process (Excel) Conversion factor: 6.894 kPa=1 PSI ºK = ºC+273.15 R= 0.286 KJ/(kg ºK) for air

7. ENTC 370PROF. ALVARADO7 Turbines and Compressors Analysis for steady state systems, Energy balance:

8. ENTC 370PROF. ALVARADO8 Problem 2: Steam Turbine (EES) Steam flows steadily (8 kg/sec, mass flow rate) through an adiabatic turbine. The inlet conditions of the steam are 10 MPa, 350 ºC, and 65 m/sec. The exit conditions are 85% quality, and 40 m/sec. The exit pressure varies from 10 kPa to 200 kPa. Determine: -Change in Kinetic Energy (  ke) -Turbine inlet area -Plot the power output against the outlet pressure P1,T1,V1 P2,x2,V2

9. ENTC 370PROF. ALVARADO9 Problem 2: Steam Turbine (EES)

10. ENTC 370PROF. ALVARADO10 Individual Lab Report Introduction: Briefly explain the objectives of the assigned tasks Data: Present data in tabulated form (use Excel) Findings or Results: Include plots (EES and Excel) for each data set and the corresponding correlation equations and correlation values Conclusions: Comment on the tasks performed and provide concluding remarks