General Physics (PHY 2130)
Lecture 36
•  The laws of thermodynamics
  Heat Engines
  Carnot cycle
http://www.physics.wayne.edu/~apetrov/PHY2130/
Lightning Review
Last lecture:
1.  Thermodynamics
  Heat and work. First Law of Thermodynamics: ΔU = Q + W
  Isothermal, adiabatic, isobaric and isochoric processes.
Review Problem: An ideal gas is in contact with a heat reservoir so that it remains
at constant temperature of 300.0 K. The gas is compressed from a volume of 24.0
L to a volume of 14.0 L. During the process, the mechanical device pushing the
piston to compress the gas is found to expend 5.00 kJ of energy. How much heat
flows between the heat reservoir and the gas, and in what direction does the heat
flow occur?
This is an isothermal process, so ΔU = Q + W = 0 (for an ideal gas) and
W = -Q = -5.00 kJ. Heat flows from the gas to the reservoir.
3
Reversible and Irreversible Processes
A process is reversible if it does not violate any law of
physics when it is run backwards in time.
Example 1: a collision between two billiard balls is
reversible. Momentum is conserved if time is run forward;
momentum is still conserved if time runs backwards.
Example 2: an ice cube placed on a countertop in a warm
room will melt. The reverse process cannot occur: an ice
cube will not form out of the puddle of water on the
countertop in a warm room.
4
Any process that involves dissipation of energy is not
reversible.
Any process that involves heat transfer from a hotter object
to a colder object is not reversible.
The second law of thermodynamics (Clausius):
Heat never flows spontaneously from a colder body to a
hotter body.
Heat Engines
•  A heat engine is a device that converts internal energy to
other useful forms, such as electrical or mechanical
energy
•  A heat engine is a device designed to convert disordered
energy into ordered energy. The net work done by an
engine during one cycle is equal to the net heat flow into
the engine during the cycle (ΔU = 0).
W net = Qnet
•  A heat engine carries some working substance through a
cyclical process
Let’s watch the movie!
Heat Engine
•  Energy is transferred
from a source at a high
temperature (Qh)
•  Work is done by the
engine (Weng)
•  Energy is expelled to a
source at a lower
temperature (Qc)
Heat Engine
•  Since it is a cyclical
process, ΔU = 0
•  Its initial and final internal
energies are the same
•  Therefore, Qnet = Weng
•  The work done by the
engine equals the net
energy absorbed by the
engine
•  The work is equal to the
area enclosed by the
curve of the PV diagram
Thermal Efficiency of a Heat Engine
•  Thermal efficiency (or simply effciency) is defined as the
ratio of the work done by the engine to the energy
absorbed at the higher temperature
net work done by the engine Wnet
e=
=
.
heat input
Qin
or
e=
Weng
Qh
=
Qh − Qc
Qh
= 1−
•  e = 1 (100% efficiency) only if Qc = 0
•  No energy expelled to cold reservoir
Qc
Qh
10
Example: (a) How much heat does an engine with efficiency of 33.3 % absorb
in order to deliver 1.00 kJ of work? (b) How much heat is exhausted by the
engine?
Idea: use the formula for the efficiency of the heat engine:
Wnet
1.00 kJ
QH =
=
= 3.00 kJ
e
0.333
(b) How much heat is exhausted by the engine?
e = 1−
QC
QH
QC = (1 − e ) QH = 2.00 kJ
Second Law of Thermodynamics
•  It is impossible to construct a heat engine that,
operating in a cycle, produces no other effect than the
absorption of energy from a reservoir and the
performance of an equal amount of work
•  Means that Qc cannot equal 0
•  Some Qc must be expelled to the environment
•  Means that e cannot equal 100%
Heat Pumps and Refrigerators
•  Heat engines can run in reverse
•  Send in energy
•  Energy is extracted from the cold reservoir
•  Energy is transferred to the hot reservoir
•  This process means the heat engine is running
as a heat pump
•  A refrigerator is a common type of heat pump
•  An air conditioner is another example of a heat
pump
Summary of the First and Second Laws
•  First Law
•  We cannot get a greater amount of energy out of a cyclic process
than we put in
•  Second Law
•  We cannot break even
Carnot Engine
•  A theoretical engine developed by Sadi Carnot
•  A heat engine operating in an ideal, reversible
cycle (now called a Carnot Cycle) between two
reservoirs is the most efficient engine possible
•  Carnot’s Theorem: No real engine operating
between two energy reservoirs can be more
efficient than a Carnot engine operating between
the same two reservoirs
Carnot Cycle
Let’s watch the movie!
Carnot Cycle, A to B
•  A to B is an isothermal
expansion
•  The gas is placed in
contact with the high
temperature reservoir
•  The gas absorbs heat Qh
•  The gas does work WAB
in raising the piston
Carnot Cycle, B to C
•  B to C is an adiabatic
expansion
•  The base of the cylinder is
replaced by a thermally
nonconducting wall
•  No heat enters or leaves
the system
•  The temperature falls from
Th to Tc
•  The gas does work WBC
Carnot Cycle, C to D
•  The gas is placed in
contact with the cold
temperature reservoir
•  C to D is an isothermal
compression
•  The gas expels energy QC
•  Work WCD is done on the
gas
Carnot Cycle, D to A
•  D to A is an adiabatic
compression
•  The gas is again placed
against a thermally
nonconducting wall
•  So no heat is exchanged with
the surroundings
•  The temperature of the gas
increases from TC to Th
•  The work done on the gas is
WCD
Carnot Cycle, PV Diagram
•  The work done by the
engine is shown by the
area enclosed by the
curve
•  The net work is equal to
Qh - Qc
Efficiency of a Carnot Engine
•  Carnot showed that the efficiency of the engine
depends on the temperatures of the reservoirs
TC
ec = 1 −
Th
•  Temperatures must be in Kelvins
•  All Carnot engines operating between the same two
temperatures will have the same efficiency
Notes About Carnot Efficiency
•  Efficiency is 0 if Th = Tc
•  Efficiency is 100% only if Tc = 0 K
•  Such reservoirs are not available
•  The efficiency increases at Tc is lowered and as Th is raised
•  In most practical cases, Tc is near room temperature, 300 K
•  So generally Th is raised to increase efficiency
Real Engines Compared to Carnot
Engines
•  All real engines are less efficient than the Carnot engine
•  Real engines are irreversible because of friction
•  Real engines are irreversible because they complete cycles in
short amounts of time
24
Example: An engine operates between temperatures 650 K and 350 K at 65.0%
of its maximum efficiency. (a) What is the efficiency of this engine? (b) If
6.3×103 J is exhausted to the low temperature reservoir, how much work does
the engine do?
(a) The maximum possible efficiency is
TC
350 K
er = 1 −
= 1−
= 0.462.
TH
650K
The engine operates at e = 0.65er = 0.30 or 30% efficiency.
(b) The heats exchanged at the reservoirs are related to each other through
QC = (1 − e)QH .
Wnet = QH − QC
QC
⎛ e ⎞
=
− QC = ⎜
⎟ QC = 2.7 kJ
(1 − e)
⎝ 1 − e ⎠