AP Physics – 1st Law Continued
1.
Collect and read the handout on Heat Engine Efficiency from
the front of the room
2. When finished work your way through the worksheet provided
3. In 20 minutes, we will explore PV diagrams and the Carnot
Cycle
4. Next Class: The 2nd Law of Thermodynamics
PV-Diagrams
Pressure/Volume graphs are of
tremendous value in analyzing
the performance of heat engines.
Essentially, the amount of work
produced by an engine depends
on the path it takes (changes in
pressure and volume)
PV-Diagrams
Confused…?
Expected, let’s start slow
1.
Engines follow a path, in this
case from 1 2, 23, 34,
and 41
2. Each affects the Work done
by, or done on the System
Net Work of a Machine
Let’s study the engine to the
right…
P
Q: is the direction of the arrows
P2
important?
P1
c
d
a
b
V1
V2
V
Net Work of a Machine
Let’s study the engine to the
right…
Q: is the direction of the arrows
important?
YES! Challenge is if work is done
ON the system or BY the system
Note: Please write down the work
done for each of the next for steps
P
P2
P1
c
d
a
b
V1
V2
V
Step 1: Process a  b represents an isobaric
compression of a gas
From a to b, the pressure remains
constant – its value is P1.
P
The volume decrease from V1 to
V2.
This represents work done on the
system.
How can you calculate the W?
P1
a
b
V1
V2
V
Step 1: Process a  b represents an isobaric
compression of a gas
From a to b, the pressure remains
constant – its value is P1.
P
The volume decrease from V1 to
V2.
This represents work done on the
system.
How can you calculate the W?
W = PDV
(
= P1 V1 -V2
)
P1
a
b
V1
V2
V
Step 2: Process b  c is an isochoric
compression
Isochoric because the volume
does not change but the pressure
increases.
What is the work for this step?
P
P2
c
0!!!
P1
b
V1
V
Step 3: Process c  d is an isobaric expansion.
The gas expands from V1 to V2,
doing work as it expands. The
amount of work is equal to the
area under the curve.
W = PDV
(
= P2 V2 -V1
P
P2
c
d
)
V1
V2
V
Step 4: Process d  a is an isochoric expansion
Volume stays constant. So no
work is done. Pressure decreases.
W = PDV
()
=P 0
=0
P
P2
P1
c
d
a
b
V1
V2
V
Complete Cycle
Based on what you have recorded
for the work on each step, what is P
the total work done on the
system?
P2
P1
c
d
a
b
V1
V2
V
Complete Cycle
Based on what you have recorded
for the work on each step, what is P
the total work done on the
system?
P2
(
W = P2 V2 -V1
)
(
- P1 V1 -V2
c
d
)
OR just the area of the enclosed
area!
P1
a
b
V1
V2
V
Whiteboarding!
1.
Form a group of 3 or 4 no more no less
2. Collect a Whiteboard and pens, and work your way through the
following two problems
3. Make sure you are contributing to your group, if you are not
then start a new group!
Question 1:
A substance undergoes a cyclic
process shown in the graph. Heat
transfer occurs during each process
in the cycle.
(a) What is the work output during
process a  b?
P ( atm)
a
5 .0 0
(b) How much work input is
required during process b  c? 1.0 0
c
(c) What is the net work done
during the cycle
10 .0
Note: 1 atm = 1.013 x 105 Pa
Note: 1 L = 0.001 m-3
b
5 0 .0
V (L)
Question 1:
A substance undergoes a cyclic process
shown in the graph. Heat transfer
occurs during each process in the cycle.
(a) 1.22 x 104 J (Expansion process, so
work is done on surroundings)
P ( atm)
a
5 .0 0
(b) -4.05 x 103 J
(c) -8.15 x 103 J
1.0 0
c
10 .0
b
5 0 .0
V (L)
Question 1:
Question 2:
A heat engine’s cycle is shown in
the PV diagram to the right.
P
P1 = 345 kPa, P2 = 245 kPa, P3 = 125
P1
k Pa, and P4 = 225 kPa. V1 = 35.0 L
P2
and V2 = 85.0 L.
What is the net work done during
one cycle of the engine?
P4
P3
a
b
d
c
Note: 1 L = 0.001 m3
V1
V2
V
Question 2:
A heat engine’s cycle is shown in
the PV diagram to the right.
P1 = 345 kPa, P2 = 245 kPa, P3 =
125 k Pa, and P4 = 225 kPa. V1 =
35.0 L and V2 = 85.0 L.
What is the net work done
during one cycle of the engine?
P
P1
a
P2
P4
P3
b
d
c
Note: 1 L = 0.001 m3
Ans: 6.00 kJ
V1
V2
V
Question 2:
1st Law + Carnot Cycle – An Ideal Engine
1.
Please put away the whiteboards
2. Collect the 1st Law Up to Now Worksheet + the handout on
the Carnot Cycle, make sure to read this!
3. By now you should have complete most of the MC questions
from the Thermo Package
4. We will have our last quiz in 20 minutes!
1st Law incomplete
• Conservation of Energy, however processes that do conserve
energy, still don’t appear to happen! WHY!?
A coffee cup breaks spontaneously but is unable to get put back
together spontaneously
Clausius statement: “it is impossible for a self acting machine
working in a cyclic process without any external force, to transfer
heat from a body at a lower temperature to a body at a higher
temperature.”
Engine Efficiency
“Engine Statement”
It is impossible for any system to
undergo a process in which it absorbs
heat from a reservoir at a single
temperature and converts the heat
completely into mechanical work, with
the system ending in the same state in
which it begins.
Workless Refrigerator
“Refrigerator Statement”:
It is impossible for any process to
have as its sole results the transfer of
heat from a cooler to a hotter body
2nd Law of Thermodynamics
Efficiency ≠ 100%
The Carnot Cycle represents the
MAXIMUM efficiency for a heat engine
1.
Isothermal exp.
2.
Adiabatic exp.
3.
Isothermal comp.
4.
Adiabatic comp.
Efficiency of Carnot Cycle
TH - TC
ecarnot =
x100%
TH
eheat engine £ ecarnot
Quiz! ~ Heat Engines
Please set up for 4th and final quiz
More Handouts!
• Please collect three more handouts on Efficiency of Engines, the
Second Law and…
• AP Thermodynamics Wrap-up that reviews all the equations and
how the work… VERY USEFUL!
• Next Class: Thermo Unit Test
AP Physics Tutorial: Next Tuesday Morning at 7:30-8:15 AM Please bring questions! If
you’re at home we will be doing a Socrative Review! Please log in and take it!