Transcript Polytropic Process(1)
ENTC 370
THERMODYNAMICS LAB Mass and Energy Analysis of Control Volumes Polytropic Processes
ENTC - 370 PROF. ALVARADO 1
Polytropic Process(1)
• During expansion and compression processes of gases, the following relationship holds:
PV n
=
C
1 If m is constant, m n is also constant V n P
Pv
m n
n
= =
C
2
C
2 Equation_ 1 For a Process from state 1 to state 2:
P
1
v
1
n
=
P
2
v
2
n
• The coefficient n depends on the process.
2
Polytropic Process(2)
• During expansion and compression processes of gases, the following relationship holds: Taking natural log_ of_ Equation_ ln(P) n ln(
v
) C Y ln(P); X ln(
v
) Y -n X C 1 : If we measure T and P, we can_ obtain_ v_ from_ Ideal_ gas_ equation :
PV
mRT
V m
R T P
v
R T P
• The coefficient n depends on the process.
3
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.
ENTC 370 Graph from www.taftan.com
PROF. ALVARADO 4
Polytropic Process
• Boundary work:
W b W b
( 2 1
n
T
1 ) n
PV
ln
V
2
V
1 n=1 1 ENTC 370 PROF. ALVARADO 5
Problem 1: Polytropic Process (Excel)
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, corresponding
P Pv = RT,
. Use SI units:
m3/kg
for to compute
v,
k
Pa
for
v P and
for each
ºK for T
.
Conversion factor: 6.894 kPa=1 PSI ºK = ºC+273.15
R= 0.286 KJ/(kg ºK) for air 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 compare with
n n
values, that is, how do the
n
values values for other, known processes (see previous slide)?
ENTC 370 PROF. ALVARADO 6
Turbines and Compressors
• Analysis for steady state systems, Energy balance: For Adiabatic Turbines in
out
(
h
1
ke
v v
1 2 1 2 2
v
2 2
gz
1 ) 2
out
: (
h
2
v
2 2 2
gz
2 ) ENTC 370 PROF. ALVARADO 7
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.
P1,T1,V1 Determine: -Change in Kinetic Energy ( ke) -Turbine inlet area P2,x2,V2 -Plot the power output against the outlet pressure ENTC 370 PROF. ALVARADO 8
ENTC 370
Problem 2: Steam Turbine (EES)
V
v
A where
,
m V
mass
_
flow
_
rate
Volume
_
flow
_
rate v
velocity
specific
_
volume A
cross
_ sec
tional
_
area
PROF. ALVARADO 9
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 ENTC 370 PROF. ALVARADO 10