1. EGR 334 Thermmodynamcis Chapter 3: Section 15
Lecture 11:
Polytropic Processes
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2. Main concepts for today’s lecture:
Polytropic Process is defined and explained
Let’s do some example problems.
Reading Assignment:
Read Chap 4: Sections 1-3
Homework Assignment:
From Chap 3: 138, 142,144,147

3. What is a polytropic process?
Sec : Incompressible Substance Model
What is a polytropic process? or
The exponent, N, may take on any value from -∞ to + ∞,
but some values of N are more interesting than others.
N= 1: Isothermal process
N= 0: Isobaric process

4. What is a polytropic process?
Sec : Incompressible Substance Model
What is a polytropic process? or
The exponent, N, may take on any value from -∞ to + ∞,
but some values of N are more interesting than others.
N= k: Adiabatic process
N≠ 1: most polytropic processes

5. Problem T or F.
a) T or F: The change in specific volume from saturated liquid to saturated vapor (vg - vf) at a specified saturation pressure increases as the pressure decreases T
b) T or F: A two phase liquid-vapor mixture with equal volumes of saturated liquid and saturated vapor has a quality of 50% F
c) T or F: The following assumptions apply for a liquid modeled as incompressible: the specific volume is constant and the specific internal energy is a function only of temperature. T
d) T or F: Carbon dioxide (CO2) at 320 K and 55 bar can be modeled as an ideal gas. ( pr = Tr = Z = ) F
e) T or F: When an ideal gas undergoes a polytropic process with n=1, the gas temperature remains constant T

6. Example Problem: (3.139) One kilogram of air in a piston cylinder assembly undergoes two processes in series from an initial state where
p1_gage = 0.5 MPa, and T1 = 227 deg C.
Process 1: Constant temperature expansion until the volume is twice the initial volume.
Process 2: Constant volume heating until the pressure is again 0.5 MPa.
Sketch the two processes in series on a p-v diagram. Assuming ideal gas behavior, determine
a) the pressure at state 2.
b) the temperature at state 3
c) the work and heat transfer for each process.

7. P-v diagram m = 1 kg of air State 1:v p 2 1 3
m = 1 kg of air
State 1:
p1 = 0.5 MPa MPa = MPa
T1 = 227 deg C.= 500 K
State 2:
T2 = T1 = 227 deg C. = 500 K
V2 = 2V1
Apply 1st Law of Thermo:
Process 1-2: constant T
ΔU1-2=Q1-2 - W1-2
Process 2-3: constant V
ΔU2-3=Q2-3 - W2-3
State 3:
p3 = p1 = MPa
V3 = V2

8. m = 1 kg of air R= 0.2870 kJ/kg-K Apply Ideal Gas Law: State 1:v p 2 1 3
Apply Ideal Gas Law:
State 1:
p1 = MPa T1 = 500K
State 2:
T2 = 500 K V2 = 2V1 = m3
State 3:
p3 = p1 = MPa V3 = V2 = m3

9. m = 1 kg of air R= kJ/kg-K
State 1: p1 = MPa T1 = 500K V1= m3
State 2: p2= MPa T2 = 500 K V2 = m3
State 3: p3 = MPa T3 = V3 = m3
Process 1-2:
where:
for constant T: and

10. m = 1 kg of air R= kJ/kg-K
State 1: p1 = MPa T1 = 500K V1= m3
State 2: p2= MPa T2 = 500 K V2 = m3
State 3: p3 = MPa T3 = V3 = m3
Process 2-3:
where: so
for constant T:

11. End of slides for Lecture 11