**General comments**

This was the last thermodynamics lecture. I discussed the differences
between reversible and irreversible processes and provided the equations necessary
to calculate entropy changes for a system. A few notes: We define an irreversible
process as one that cannot be reversed without some change to the surroundings
(typically, work going to heat). Reversible processes are useful idealizations
and we use them for comparison to measure how well we are doing with real (irreversible)
processes. When we measure the entropy changes of *both* the system and
the surroundings, the sum tells us how much irreversibility we have (how far
from ideal we are). The amount of irreversibility is directly related to a lost
opportunity to do work. Entropy is a convenient combination of thermodynamic
properties (and is thus a thermodynamic property itself). On the final
homework, you will get some practice calculating changes in entropy for
a system. You have not been given the tools to calculate the change in entropy
for the surroundings. You will get to this in 16.05.

__Final note:__ I very much enjoyed
teaching you over the last month. I look forward to seeing you all again during
the spring when I teach the propulsion material. In preparation for the quiz,
if you have any questions at all, please contact me. I would be happy to set
up a meeting to go over the material with you.

Additional opportunities to talk with me:

4-5pm Monday during office hours

9-10 and 10-11 on Thursday during recitation.

**Responses to 'Muddiest Part of the Lecture Cards'**

(43 respondents out of 66 students attending class)

1)* Do we need to derive the entropy
equation? Could you please post an entropy type question on the muddy responses?--and
related questions *(2 students). No, you do not
need to be abe to derive the entropy equation. What I would like you to know
about entropy is that it is a property--a function of the state of the system.
It is useful to us because we can use it to measure the degree of irreversibility
in a process (by looking at entropy changes of the system and surroundings).
And the amount of irreversiblity is related to the work we get out of a process
(compared to an ideal process). An "entropy type" question would either
be to describe what entropy is and why it is useful to us, or to calculate the
entropy change of a system during a process (like homework
T12). You will not learn how to calulate the entropy change of the surroundings
until you get to 16.05.

2) * What about heat exchangers? We
didn't cover them explicitly, but are we supposed to put 2 and 2 together on
the quiz?* (1 student) They are covered explicitly on homework
T11. You are expected to understand the basics of the energy exchange processes
in a heat exchanger for the quiz. If you have questions, please contact me.

3) * Could you demonstrate a problem
using entropy and show a graph of T-s? -- and related questions*
(3 students). You will have an opportunity to do this on homework
T12. That is about as much as I would expect you to know at
this point. I would be happy to do another example in the next recitation.

4) * How will entropy be used in an
engineering field?* (1 student) We will use it as a measure of
irreversibility or lost work, i.e. to compare the efficiency of our processes
to ideal processes.

5) * Are there any other useful equations
that I should know for entropy? I thought there was some way to calculate s
using H and delta T? (or was that Gibb's free energy?)* (1 student)
For now, stick with the equations given in the notes. My objective in this lecture
was just to introduce a useful new property and note that we could use it as
a measure of irreversibility. When you get to 16.05 and start solving many problems
using entropy, you will see there are some other very useful relations.

6) * I didn't understand how entropy
is defined. Isn't it the loss of energy due to natural dissapation?*
(1 student) No. Energy is a property, entropy is a property. Energy is not lost,
but conserved (the first law). Entropy changes are related to how much work
we can get out of a system (an energy transfer across the system boundary) compared
to the maximum possible work for an ideal process. These concepts may be a little
obscure right now, because you don't quite have all the tools necessary to use
entropy changes to measure the lost opportunity to do work.

7) * I have read that entropy is always
increasing and that at maximum entropy...nothing will be able to happen (no
change)...will we learn about this in 16.05? Also, wouldn't all REAL systems/processes
have some entropy or else we could create a pertetual motion machine?*
(1 student) In response to your first question, yes entropy is always increasing.
I think the maximum would have to coincide with no more opportunity to do work
-- e.g. the entire universe at the same state. We are a long way away from this
however. And while it is interesting to think about, there are other more practical
purposes for measuring entropy changes, i.e. to assess the performance of devices.
You will learn about doing this in 16.05, but probably not about what happens
at the end of the universe. In response to your second question. All systems
have entropy (it is a property and a function of the state of the system. All
real processes produce entropy changes (when summed up for the system and the
surroundings). And yes, an ideal energy exchange process with no change in entropy
(again, when the change is measured for both the system and the surroundings)
would allow a perpetual motion machine.

8) * A system is reversible if delta
w=0, even though delta q not equal zero? Why?* (1 student). A

9) * For an isothermal compression,
how do you find the heat and work? I keep getting it wrong.* (1
student) Qualitatively, you can obtain the sign for work by noting that the
specific volume decreases during the process (negative work). Then applying
the first law for an ideal gas, if delta T = 0 (since isothermal), then q=w.
So you know that heat and work are numerically equal. In terms of finding a
numerical answer, the details are given in the notes.

10) * Does the turbine extract work
from the gas and the compressor do work on the gas so that the shaft work for
a compressor is positive and the shaft work for a turbine is negative?-- and
related questions* (2 students) The turbine extracts work from
the gas (our system). So the system does work when passing through a turbine
(positive work). The opposite is true of a compressor. The system has work done
on it (negative work). To avoid confusion, remember that the system is the gas.

11) * Can you describe the work and
heat transfer of the engine failure (with water and blades) to give us some
experience with what to look for?* (1 student) Sure. Here
it is.

12) * Is there any chance of holding
a quick review session Wed. or Thurs.?* (1 student) The recitations
on Thursday are intended to serve this purpose.

13) * So what is the deal with entropy
and religion?* (1 student) Entropy is a very useful property with
broad applications in many fields. It also is rather obscure to many people.
It can also be confusing to many people because it isn't a property that is
commonly measured and quoted on the news every day (like temperature). It also
has implications for many of the broader processes we observe in the universe.
As a result of all of the above, the concepts of entropy, entropy changes and
implications for processes we observe around us have been embraced to varying
degrees and with varying interpretations by many people--all independent of
the connection to religion. The connection with religion is secondary, but tends
to find its way into the news. There are many expert thermodynamicists with
very strong faith throughout the world, and other people of very strong faith
who don't embrace some of the implications of the second law of thermodynamics.

14) * No mud. * (26 students)
Great.

1)* When two different temperature
bricks are put together, how is the process reversed? How does net work become
zero? *(1 student)
I assume you are asking how to make this process reversible. The way to do this
is with a whole series of reserviors that are each only a small delta T different
in temperature. Then it is possible to gradually transfer the heat from one
brick to another and then go in reverse. You will learn more about this in 16.050

2) * I didn't
exactly understand the difference between the two processes (rev. and irrev.)
on the board. Was the difference that the piston was included in one so you're
not changing the surroundings to reverse?* (1 student) First,
review the notes. The difference is that in the
reversible case when the system is returned to its initial state, the surroundings
are too. In the irreversible case, even though the system is returned to its
initial state, the surroundings have been changed.

3) * A good example
to use in the future is two pistons with a shaft connecting the two. It shows
that work is saved in the other piston when one expands.* (1 student)
Very good suggestion. Thank you. It is like a thermodynamic pendulum.

4) * If all processes
conserve energy, then why aren't all processes reversible?* (1
student). Conservation of energy is not a sufficient condition for a process
to be reversible. It is rather the other way around. All real processes are
irreversible. In our world, physical processes like friction etc., lead to additional
work being required to return systems to their initial state.

5) * Would like
more examples on entropy and reversible processes. How do you measure inefficiency
of a system analyzing entropy?* (1 student) I can give you more
examples in recitation. Relative to measuring efficiency using entropy, this
is a topic for a later course (16.050).

6) * What parts
of entropy will be covered on the test?* (1 student) There will
be very little emphasis on entropy. For guidance read the subject
learning objectives. I would like you to understand the difference between
reversible and irreversible processes and why the difference is important for
engineering devices. You should be able to state that entropy is a property
and a function of the state of the system and is used to measure how irreversible
various processes are (as you will see in homework
T12).

7)* T-s diagram
-- How is it used to understand efficiency? *(1 student) That
is beyond the scope of this course. If you are interested you can read ahead
in one of the textbooks on reserve in the library or wait for 16.050.

8) * No mud. * (26 students).
Very good.