Single
atom heat engine as a sensitive thermal probe.
A single atom heat engine has a sensitive thermal probe
preparation and manipulation of quantum systems for the design of new
technology require the ability to detect the influence of physical properties
of the environment with high precision however many of the variables cannot be
measured directly as they are not proper quantum observable and must be instead
inferred from indirect measurements the temperature of the system is such a
property on the other hand the emerging fields of thermodynamics in the quantum
regime sheds new light on energy exchange processes between interactive. Small
quantum systems under environment manipulating these interactions in a
structural manner reveals simple laws that relates property of the environment
to observable of the quantum system.
For
example.
The power output of a depends on the temperature difference
of the bath using this concept we design a temperature sensor to understand the
working principle of here we see the water wheel that spins due to the river
flow in this sense we can consider the river as an engine that produce work.
Thanks to the water gradient this output work is employed to move a wheel in
our quantum model the engine and the wheel are replaced by a trapped ion.
Radial degree
Its radial degree of freedom acts as an engine the output
work is provided by the temperature gradient produced by two separated thermal
baths that interact with the ion when this is moved to these locations leading
to an engine cycle on the other hand this output work is transferred to the
axial degrees of freedom that mimics the wheel and make the ion oscillate in
this direction due to the coupling nature between the ion and the baths the
oscillations grow linearly Every time the engine performs a cycle.
The
cycling nature
The cycling nature of the engine allows transforming the
small bath-temperature differences into macroscopic oscillations of the
flywheel in an inverse perspective measuring these oscillations allows us to
use this engine as a sensitive thermometer as the generated output depends on
the relative temperature differences if one of the bath is known then other is
fully determined
The
working principle of our model
Once we have explained the working principle of our model
now let's move to the lab for the experimental details this project started
2016 when we did the smallest heat engine with a single ion now this project is
funded by the research unit thermal machines in the quantum world and the
details are following in this lab we are running a single atom heat engine our
system is a single calcium ion trapped in a linear Paul trap we did a
modification to the power trap so that our radio frequency electrode are tilted
to the symmetry axis of the trap by a small angle and this tilt induces a small
coupling between the radial state and the actual motion of the ion the working
principle of the heat engine is thus simple depends on the temperature of the
radial state the ion experiences a different displacement force in the actual
direction so if we periodically switch the temperature of the radial state we
excite a coherent motion in the axial direction which serves as the energy
output of the engine the cold path is implemented by applying Doppler cooling
to the iron and a hot bath is employed by applying noise as well on the DC
compensation electrodes then the engine is run for a number of cycles and after
this by simply taking a picture for a brief period of time we can estimate the
position of the ion and therefore determine the growth of the amplitude and
therefore determine the temperature difference.
Heat
engine vs Heat pump
We are going to compare Heat engine, Heat pump and
Refrigerator on basis of efficiency and coefficient of performance we also
derive equation of Conform heat pump and refrigerator.
Here heat engine is used to perform work. Where heat pump is
used for heating purpose in cold region and refrigerator is used for cooling
purpose in hot region In heat engine
Question
about heat engine
Q1 amount of heat is added to the system that is we burn
fuel in heat engine to produce thermal energy to perform some useful work which
is net work done by the engine.
Q2 amount of heat is rejected. That is heat of exhaust gases
out of engine cylinder so to calculate efficiency of engine.
Here we have the formula that is output upon input so here
output is net work done and input is heat added to engine therefore the formula
is Q1 minus Q2 upon Q1 and here Q1, Q1 get canceled, and we will get efficiency
of engine as none minus Q2 by Q1.
In
case of refrigerator
we extract heat from cold region and maintain cold region to
low temperature because the purpose of refrigerator is to cool the system
therefore here we provide work by means of compressor here the COP that is
coefficient of performance is the ratio of heating effect or cooling effect to
the work input in refrigerator cooling effect is Q1 that is we extract Q1
amount of heat from cold region and reject Q2 amount of heat to hot region so
difference of Q2 minus Q1 is work input and here work input is compressor work
therefore COP for refrigerator is equal to cooling effect that is Q1 upon work
inputnwhich is Q2 minus Q1
Heat Pump
Now heat pump is the device here we take out heat from cold
body which is Q1 and deliver heat to the hot body the delivered heat is Q2
therefore COP of heat pump is the amount of heat is rejected that is Q2 upon
net work done which is Q2 minus Q1 now here we have to derive the equation that
is COP for pump is equal to one plus COP for refrigerator and here is the
formula of COP for refrigerator is Q1 by Q2 minus Q1 minus Q1 plus Q1 get
canceled, and we will get the formula of COP for heat pump that is Q2 minus Q1
in this way we prove that COP of heat pump is greater than one
How to
make a project with heat engine
Here's a neat heat engine made using material from a coffee
bag, and that sort of opens and closes like a flower. The petals of the
rotating part are strips cut from the coffee bag. Behind it on one side is a
glass of hot water, meaning the air around is it hot, and on the other side is
a glass of cold water, with cold air surrounding it. You can see the petals
straighten out in the hot air, .and curl back up in the cold air, making it an
unbalanced wheel that keeps on rotating. It's pretty simple to make and in this
video I'll show you how.For the stator, I've made this stand with scrap wood.
And two stiff scrap aluminum bars. In this bar I've made a tiny indentation
near the top. I attach some neodymium magnets to one bar, and tape some more to
the other bar For the rotor, I've cut this round plastic disk, and stick a
needle through it.
Next step
By putting the sharp end of the needle in the tiny
indentation, and with the help of the magnetic fields, the needle just sits
there, and turns very easily. But, the disk is unbalanced, always coming to a
stop with the same side down. So I sand away some plastic from that side. It
still isn't balanced, so I sand some more, .until finally the rotor stays
pretty much however I orient it. Then I start cutting up the coffee bag, and
cut a strip from it. The strip is 1/2" wide by 2 1/8" long. A piece
of duct tape holds it onto the disk. Then I attach another piece and make sure
they both stretch out the same distance from the center.
Next
But notice that one petal always hangs down, so the whole
thing is unbalanced. After trimming a little from the petal that was hanging
down, the rotor balances better now. I give the petals a little curvature using
the blunt edge of a pair of scissors.I then put out two glasses of water, one
hot and one cold, along with the stand and the heat engine's rotor. From the
top you can see this petal straightening out in the hot air surrounding the
glass containing hot water, and this petal curling up in the cold air surrounding
the glass containing cold water.
Heat
engine project
Eventually I add all eight petals. But notice that since
it's now heavier I've also had to add more magnets. And as you'd expect the
rotor is unbalanced again, with the same side always hanging down. To fix it
this time I add a little extra tape on the opposite side. And now it stays put
wherever I leave it. It's balanced. After using the scissors again to give all
the petals a curvature,I give it a try. All that careful measuring and balancing
has. Paid off as it works the first time. You can see the petals straighten out
on the hot side, and curl up again on the cold side.
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