Carnot cycle efficiency for heat engines.

[Dave]

This post is a follow up to a previous one, expressing a lack of belief
in the Carnot cycle efficiency for all heat engines, with the maximum
efficiency given by:
Q = 1 - Tc/Th. - temperatures in Kelvin
Tc is the cold temperature and
Th is the hot temperature

The demonstration is from using methanol then water as the working fluid
in a steam engine. It is assumed that a turbine is equally as good as
working with water steam or methanol vapour

Density of methanol vapour is 1.206 kg/m^3 at 64C
Density of steam is 0.59 kg/m^3 at 100C

So boiling 2 kg of methanol should give the same potential for work,
more or less as 1 kg of water. Assuming a good condenser/turbine.

The given belief is that the maximum theoretical efficiency is given by
Q, and I cannot disprove this without experiment. The argument below
looks at practical application in the real world.

https://www.engineeringtoolbox.com/methanol-density-specific-weight-temperature-pressure-d_2091.html
https://www.engineeringtoolbox.com/saturated-steam-properties-d_457.html

Starting at 20 Celsius.
Consider 1kg or methanol, boils at 64C

To create 1kg of vapour needs 64-20 = 44 C uplift, + the vapourization.

= 44 * 2490 + 1165 000
= 1 274 560 J.

So for 2kg need 2 549 120 J

To boil 1Kg or water:

Add the temperature uplift needed (80C and the vapourization)

= 80 x 4182 + 2.26 x 10^6 J
= 334 560 + 2.26* 10^6 J
= 2 594 560 J

So the numbers for water and methanol are about the same.

Expect water should be more efficient due to the higher temperature
from Q formula.

The thing to go now is to look at refrigerants which are good for 35-40
C. This is so that a compost heap or a lightly heated water
(easy to do -pump it from the top) can be used.

Seems like they are using isopentane already - nice properties for
compost or warmish water.
https://en.wikipedia.org/wiki/Isopentane

Unfortunately the good non flammable refrigerants got banned.

Discovering this century that some sociology and biology teachings going
back over 100 years are in the LOFS category. e.g. human evolution from
ape like creatures. Why should physics be different?

[Jim Pennino]

Post by Dave
This post is a follow up to a previous one, expressing a lack of belief
in the Carnot cycle efficiency for all heat engines, with the maximum
Q = 1 - Tc/Th. - temperatures in Kelvin
Tc is the cold temperature and
Th is the hot temperature

This has been well known for about 200 years now.

Post by Dave
The demonstration is from using methanol then water as the working fluid
in a steam engine. It is assumed that a turbine is equally as good as
working with water steam or methanol vapour

The above equation has no variables for working fluid and is valid for
all heat engines.

You are tilting at windmills.

<snip irrelevent babble>

https://en.wikipedia.org/wiki/Carnot_cycle

Especially:

https://en.wikipedia.org/wiki/Carnot_cycle#Properties_and_significance

You might also read:

https://en.wikipedia.org/wiki/Carnot_heat_engine

[Dave]

Post by Jim Pennino

Post by Dave
This post is a follow up to a previous one, expressing a lack of belief
in the Carnot cycle efficiency for all heat engines, with the maximum
Q = 1 - Tc/Th.  - temperatures in Kelvin
        Tc is the cold temperature and
        Th is the hot temperature

This has been well known for about 200 years now.

Post by Dave
The demonstration is from using methanol then water as the working fluid
in a steam engine.  It is assumed that a turbine is equally as good as
working with water steam or methanol vapour

The above equation has no variables for working fluid and is valid for
all heat engines.
You are tilting at windmills.
<snip irrelevent babble>
https://en.wikipedia.org/wiki/Carnot_cycle
https://en.wikipedia.org/wiki/Carnot_cycle#Properties_and_significance
https://en.wikipedia.org/wiki/Carnot_heat_engine

The Carnot cycle efficiency is being over applied to fluids where
there is a phase change.  Another way to look at it is the "apparent"
temperature of the condensed liquid should it be an ideal gas having
the the same volume as the liquid.

More politely, Q  = 1 - Tc/Th is an oversimplification.
Explanatory text was present to show that changing long held beliefs is
 too much of a challenge for some.

For an experiment, have water temperatures of 98C and 100C.

Q = 1 - (98+273)/(100+273) = 0.00536.

To boil 1kg of water from 98C and vapourize it takes
4198 *2 + 2.26MJ
= 2.26MJ

With a density of 0.59Kg/m^3, 1kg has a volume of 1.69 m^3
Assume this is all vacuum after condensing,
Work done by vacuum is amount of water pushed up column which can be
lifted by air pressure (about 10m depending on air pressure):
- using 1.6 m^3 to account a very thin pipe.
i.e. 10m x 9.8 x 1.6 x 1000 = 156 800 J
Ignoring vapour pressure - ideal water, or using a "membrane barrier"
Efficiency = 156 800/ 2 226 000 = 7%,

7% isn't great, but a lot better than 0.5% given by Carnot maximum
theoretical efficiency.

So could you cascade a low temperature turbine? Yes. not great
efficiency, so need to work on air float rotors - no bearings etc.
Moving parts, yes, touching moving parts no.

Thank you for your attention.

[Dave]

Post by Dave

Post by Jim Pennino

Post by Dave
This post is a follow up to a previous one, expressing a lack of belief
in the Carnot cycle efficiency for all heat engines, with the maximum
Q = 1 - Tc/Th.  - temperatures in Kelvin
        Tc is the cold temperature and
        Th is the hot temperature

This has been well known for about 200 years now.

...

Post by Dave

More politely, Q  = 1 - Tc/Th is an oversimplification.
Explanatory text was present to show that changing long held beliefs
is   too much of a challenge for some.

For an experiment, have water temperatures of 98C and 100C.
Q = 1 - (98+273)/(100+273) = 0.00536.
To boil 1kg of water from 98C and vapourize it takes
4198 *2 + 2.26MJ
= 2.26MJ
With a density of 0.59Kg/m^3, 1kg has a volume of 1.69 m^3
Assume this is all vacuum after condensing,
Work done by vacuum is amount of water pushed up column which can be
- using 1.6 m^3 to account a very thin pipe.
i.e. 10m x 9.8 x 1.6 x 1000 =  156 800 J
Ignoring vapour pressure - ideal water, or using a  "membrane barrier"
Efficiency = 156 800/ 2 226 000 =  7%,
7% isn't great, but a lot better than 0.5% given by Carnot maximum
theoretical efficiency.
So could you cascade a low temperature turbine?  Yes. not great
efficiency, so need to work on air float rotors - no bearings etc.
Moving parts, yes, touching moving parts no.
Thank you for your attention.

What is my round trip endgame?

My suburban back garden can get to have a solar water heater pond.
e.g. 24m^2. From this is can get loads of warm water on sunny days,
especially with a shallow depth. (20mm).

Three fills on a summer day, one in winter sunny day.
In summer is 24x0.02 x 3 *1000 = 1440l of 50 C water.
(enough to boil pentane), might be able to run a generator which has 5%
efficiency, get something and still have warmish water (25C). Without
Solar PV, seems like 1950s technology, but the advantage is that the
24/7 generation is built in, so not as much battery storage needed. Pond
installation is very cheap - sand base, insulation, pond liner, some
aluminium, black paint, wood, pump used intermittently, polycarbonate
cover.

A belief in Carnot efficiency stops this thinking in its tracks.

[Jim Pennino]

Post by Dave

Post by Dave

Post by Jim Pennino

Post by Dave
This post is a follow up to a previous one, expressing a lack of belief
in the Carnot cycle efficiency for all heat engines, with the maximum
Q = 1 - Tc/Th.  - temperatures in Kelvin
        Tc is the cold temperature and
        Th is the hot temperature

This has been well known for about 200 years now.

...

Post by Dave

More politely, Q  = 1 - Tc/Th is an oversimplification.
Explanatory text was present to show that changing long held beliefs
is   too much of a challenge for some.

For an experiment, have water temperatures of 98C and 100C.
Q = 1 - (98+273)/(100+273) = 0.00536.
To boil 1kg of water from 98C and vapourize it takes
4198 *2 + 2.26MJ
= 2.26MJ
With a density of 0.59Kg/m^3, 1kg has a volume of 1.69 m^3
Assume this is all vacuum after condensing,
Work done by vacuum is amount of water pushed up column which can be
- using 1.6 m^3 to account a very thin pipe.
i.e. 10m x 9.8 x 1.6 x 1000 =  156 800 J
Ignoring vapour pressure - ideal water, or using a  "membrane barrier"
Efficiency = 156 800/ 2 226 000 =  7%,
7% isn't great, but a lot better than 0.5% given by Carnot maximum
theoretical efficiency.
So could you cascade a low temperature turbine?  Yes. not great
efficiency, so need to work on air float rotors - no bearings etc.
Moving parts, yes, touching moving parts no.
Thank you for your attention.

What is my round trip endgame?
My suburban back garden can get to have a solar water heater pond.
e.g. 24m^2. From this is can get loads of warm water on sunny days,
especially with a shallow depth. (20mm).
Three fills on a summer day, one in winter sunny day.
In summer is 24x0.02 x 3 *1000 = 1440l of 50 C water.
(enough to boil pentane), might be able to run a generator which has 5%
efficiency, get something and still have warmish water (25C). Without
Solar PV, seems like 1950s technology, but the advantage is that the
24/7 generation is built in, so not as much battery storage needed. Pond
installation is very cheap - sand base, insulation, pond liner, some
aluminium, black paint, wood, pump used intermittently, polycarbonate
cover.
A belief in Carnot efficiency stops this thinking in its tracks.

Real science stops a lot of crackpot thinking in its tracks.

Try reading a thermodynamics book.

[Thomas 'PointedEars' Lahn]

Post by Dave
For an experiment, have water temperatures of 98C and 100C.
Q = 1 - (98+273)/(100+273) = 0.00536.

We do not actually use the symbol Q for efficiency, but for heat instead.
As I already told you, η (eta) is the commonly used symbol for efficiency;
especially in the Carnot process where we must carefully distinguish between
heat and efficiency.

Post by Dave
To boil 1kg of water from 98C and vapourize it takes
4198 *2 + 2.26MJ
= 2.26MJ

Not quite. First you have to heat it from 98 °C by 2 K in the liquid phase
(this is actually only possible at standard pressure at sea level; any
further up and the water already boils at a temperature lower than 100 °C).
Assuming that to happen at constant pressure, the required heat is

ΔQ₁ = m c_p ΔT = 1 kg · 4181.3 J/(kg K) · 2 K = 8362 J,

where I have assumed that we can use the specific heat capacity of the
liquid phase at 100 °C since the original temperature is already close to
that.

<https://en.wikipedia.org/wiki/Table_of_specific_heat_capacities>

Then you have to effect the phase change from liquid to gaseous, which
requires the enthalpy of vaporization ΔH_vap = 2257 J/g:

ΔQ₂ = m ΔH_vap = 1 kg · 2257 J/g
= 1 kg · 2.257 kJ/g
= 1 kg · 2.257 MJ/kg
= 2.257 MJ.

<https://en.wikipedia.org/wiki/Enthalpy_of_vaporization>

But what you are overlooking here is that *if* there is a phase change, then
it does not only happen in one direction in the Carnot process as that
process also includes isothermal and adiabatic *expansion*. And the
enthalpy of condensation, which is equal in magnitude to the enthalpy of
vaporization, is actually released when the substance changes from the
gaseous to the liquid phase again.

Also, this calculation applies only to constant pressure (then you must use
c_p) or volume (then you must use c_V), and a key property of the Carnot
process is that *neither* the pressure nor the volume are constant (it is
precisely the change of volume that produces the work or vice-versa).

IOW, the (enthalpy of the possible) phase change is completely irrelevant to
the efficiency of the Carnot process. Which is why it does not matter that
the coolant in a refrigerator vaporizes and condensates all the time.

Post by Dave
With a density of 0.59Kg/m^3, 1kg has a volume of 1.69 m^3

Approximately, yes.

<https://www.wolframalpha.com/input?i=water+vapor+density>

Post by Dave
Assume this is all vacuum after condensing,

Word salad.

Post by Dave
Work done by vacuum […]

You do not know what you are talking about.

In vacuum, water already boils at temperatures well under 20 °C:

<ttps://www.wolframalpha.com/input?i=water+phase+diagram>


PointedEars

[Jim Pennino]

Post by Dave

Post by Jim Pennino

Post by Dave
This post is a follow up to a previous one, expressing a lack of belief
in the Carnot cycle efficiency for all heat engines, with the maximum
Q = 1 - Tc/Th.  - temperatures in Kelvin
        Tc is the cold temperature and
        Th is the hot temperature

This has been well known for about 200 years now.

Post by Dave
The demonstration is from using methanol then water as the working fluid
in a steam engine.  It is assumed that a turbine is equally as good as
working with water steam or methanol vapour

The above equation has no variables for working fluid and is valid for
all heat engines.
You are tilting at windmills.
<snip irrelevent babble>
https://en.wikipedia.org/wiki/Carnot_cycle
https://en.wikipedia.org/wiki/Carnot_cycle#Properties_and_significance
https://en.wikipedia.org/wiki/Carnot_heat_engine

The Carnot cycle efficiency is being over applied to fluids where
there is a phase change.  Another way to look at it is the "apparent"
temperature of the condensed liquid should it be an ideal gas having
the the same volume as the liquid.

More politely, Q  = 1 - Tc/Th is an oversimplification.
Explanatory text was present to show that changing long held beliefs is
 too much of a challenge for some.

For an experiment, have water temperatures of 98C and 100C.
Q = 1 - (98+273)/(100+273) = 0.00536.
To boil 1kg of water from 98C and vapourize it takes
4198 *2 + 2.26MJ
= 2.26MJ
With a density of 0.59Kg/m^3, 1kg has a volume of 1.69 m^3
Assume this is all vacuum after condensing,
Work done by vacuum is amount of water pushed up column which can be
- using 1.6 m^3 to account a very thin pipe.
i.e. 10m x 9.8 x 1.6 x 1000 = 156 800 J
Ignoring vapour pressure - ideal water, or using a "membrane barrier"
Efficiency = 156 800/ 2 226 000 = 7%,
7% isn't great, but a lot better than 0.5% given by Carnot maximum
theoretical efficiency.

That is because you do not understand the Carnot maximum theoretical
efficiency, what it means, or what it applies to as your "experiment"
clearly shows.

In the real world, the efficiency of a thermodynamic engine will
alwasys be less than the Carnot maximum.

[Sylvia Else]

Post by Dave
This post is a follow up to a previous one, expressing a lack of belief
in the Carnot cycle efficiency for all heat engines, with the maximum
Q = 1 - Tc/Th.  - temperatures in Kelvin
    Tc is the cold temperature and
    Th is the hot temperature
The demonstration is from using methanol then water as the working fluid
in a steam engine.  It is assumed that a turbine is equally as good as
working with water steam or methanol vapour
Density of methanol vapour is 1.206 kg/m^3 at 64C
Density of steam is 0.59 kg/m^3 at 100C
So boiling 2 kg of methanol should give the same potential for work,
more or less as 1 kg of water. Assuming a good condenser/turbine.
The given belief is that the maximum theoretical efficiency is given by
Q, and I cannot disprove this without experiment. The argument below
looks at practical application in the real world.
https://www.engineeringtoolbox.com/methanol-density-specific-weight-temperature-pressure-d_2091.html
https://www.engineeringtoolbox.com/saturated-steam-properties-d_457.html
Starting at 20 Celsius.
Consider 1kg or methanol, boils at 64C
To create 1kg of vapour needs 64-20 =  44 C uplift, + the vapourization.
= 44 * 2490 + 1165 000
= 1 274 560 J.
So for 2kg need 2 549 120 J
Add the temperature uplift needed (80C and the vapourization)
= 80 x 4182 + 2.26 x 10^6 J
= 334 560 + 2.26* 10^6 J
= 2 594 560 J
So the numbers for water and methanol are about the same.

You don't want to condense, and then later boil, your working fluid.
Doing so just pointless throws away energy that you then have to add
back, to no benefit.

Carnot provides no guidance on relative efficiencies if you're foolish
enough to do so.

So all you're doing is arguing that the difference in temperature is not
necessarily the deciding factor when it comes to the efficiency of a bad
design, and Carnot does not say otherwise, since it does not deal with
phase changes.

Sylvia.