Download Entropy - BYU Physics and Astronomy

Heat Engines
do work from heat energy taken from hot
region and exhausted to a cold region
Efficiency e =
Refrigerators
Heat engine in reverse
An engine gets 30 J of heat from burning natural gas each
cycle Its efficiency is 15%. What are |W| and Qc each
cycle?
If the engine turns at 5000 rpm, what is the power output?
Carnot engine
Most efficient possible
Only for this
ideal engine:
Qc Tc

Qh Th
so
Tc
e  1
Th
Efficiency of any real engine
obeys:
Tc
e  1
Th
Real life efficiencies
Car engines
Heat expelled: 70%
Typical efficiency: 30%
(5% later lost to air, tire friction) only 25% left for acceleration
Best gas-fired electrical plants
One heat engine: 30%
with second heat engine using exhaust heat 50-60%
Human bodies
Typical efficiency (food energy to work): 20%
Current trends
Are electric cars “efficient”?
Are hydrogen powered cars “efficient”?
P1. If you exhaust heat to the air,
your car should run most efficiently
when it is ____ and the air is ____
a) cold, cold
b) cold, hot
c) hot, cold,
d) hot, hot
e) doesn’t matter
2nd Law of thermodynamics
Engines cannot be perfectly efficient (e < 1; must
exhaust some heat to get work)
You can’t move heat from cold to hot region unless you
supply work (run a refrigerator)
The entropy of the universe must increase in any process
Entropy
Entropy (S) of a state is given by the number of
ways (W) the particles in a state can be “arranged”
S  k B ln W
(kB = 1.381 x 10-23 J/K)
Entropy is also a measure of disorder, because
disordered states can be formed in many ways.
Entropy
The most probable state is the highest entropy state
because it can be formed in many ways.
Time appears to go “forward” because we are
used to probable events occurring (and entropy
increasing)
Heat flow and entropy
When heat flows into an object that
is at T, its entropy increase is :
If heat flow out, its entropy change is
negative
Q
S 
T
P2. As ice melts, its entropy ____
a) increases, b) decreases c) stays the same.
P3. As ice melts in a normal room, the size of the
entropy change is greatest for the ____
a) ice b) room
Statistics of large numbers of
particles
Why is rolling a “7” the most probable for two dice?
As the number of dice gets large, the chance
of rolling small numbers (like all 1’s ) or large
(like all 6’s) numbers vanishes. See
www.anydice.com
4 gas particles in a box
If finding each particle in the left
or right half is random, What is
the probability we find them all on
the left half?
4 gas particles in a box
Left
Right
0
1
4
3
2
2
3
1
0
4
ways to
arrange
this (W)
Particles:
ABCD
RRRR
RRRL
RRLR
RLRR
LRRR
LLRR
LRLR
RLRL
RLLR
LRRL
RRLL
LLLR
LLRL
LRLL
RLLL
RRRR
Probability Entropy of
of this state this state
100 gas particles in a box
How much more probable is it to have the state
(50L, 50R) instead of the state (100L, 0R)?
There are about 1030 ways to arrange the
particles with 50L, 50R.
Suppose we have 100 gas particles
constrained to be all on the left by a
membrane. What is the entropy
change that happens when we
break the membrane and there are
about 50L, 50R thereafter?
(ln 10 = 2.3,
kB = 1.381 x 10-23 J/K)
P4. If you have 2 gas particles in a box. What is the
probability we find them all on the left half?
a) 1/8 b) ¼ c) ½ d) 5/16 e) 1/1
Old comedy routine on 1st and 2nd Law