Let’s say water is at the room temperature of 20 degrees centigrade and atmospheric pressure is 1 atm. At this set of (T, P) the evaporation must be happening. Why does the evaporation happen?

In the liquid, all the molecules are moving with different velocities, during their Brownian motion. The molecules which are on the surface and moving with high velocities may gain enough kinetic energy in their course of motion and collisions with other neighboring molecules, such that it is enough to break their bonds with the neighboring molecules and they are able to free themselves up from the water and come up in the air in vapor state.

These molecules when they come up in the air, take away some internal energy of the water. This internal energy is composed of two kinds of energies:
1. Kinetic energy lost by other neighboring molecules during collisions.
2. Potential energies involved in bonds between the molecules, which are now broken.

Now, since the internal energy of water decreases so its temperature also decreases, so it concludes that every evaporation process is accompanied by a decrease in temperature of the substrate.

Now when the molecules of water come up in the air, they are not free to move anywhere, even if they wish to and the thing which constraints their motion is the atmospheric pressure. Due to this atmospheric pressure, the water vapor molecules stay near the surface of the water. Some may condense back to form water, releasing some energy. The process of evaporation and condensation continues all the time and finally, a condition is reached when they reach an equilibrium. Equilibrium is the condition where the rate of evaporation and the rate of condensation become equal to each other. At this point in time, if the temperature and pressure are unaltered then the amount of water and vapor above it will remain the same till eternity.

Now if the temperature is increased, maintaining the same pressure, more molecules will gain enough kinetic energy to break free from water and come up in the vapor state, which will increase vapor pressure, which will expand the volume the vapor is occupying above the water surface, and this expansion of water vapor will, in turn, decrease its pressure, till the time it attains an equilibrium with the atmospheric pressure.

If we keep on increasing the temperature, maintaining the same atmospheric pressure, the quantity, volume and kinetic energies molecules of vapor will keep on increasing and when we reach the boiling point then it will be the time when the water molecules and the vapor molecules will have enough kinetic energies such that the pressure created by them will be increasing at a faster rate than the decrease in the pressure on the increase of volume of vapor under the pressure of atmosphere. We can understand it by an analogy. At the interface of vapor and atmosphere, the force applied by vapor will be greater now than the force applied by the atmosphere and the interface will now begin to accelerate, and this phenomenon, we have given this fancy name called “Boiling”.

Further Readings:
Difference Between Vapor Pressure and Boiling Point

The phenomenon of Boiling! was originally published in Intuitive Physics on Medium, where people are continuing the conversation by highlighting and responding to this story.

Everywhere in the literature I have across, I find that whenever the discussion of the Induced electric field comes, it is discussed around a cylindrical time-varying magnetic field. The induced electric field turns out to be circular in this case.

My question is, what shape does the induced electric field take when the magnetic field is time-varying but non-cylindrical?

Electric and magnetic field around a coil of a rectangular cross-section. Figure 1 shows the geometry of the coil, the distribution of current (red) and magnetic field (blue).

In fig. 2 shows the distribution of the magnetic field in various sections y=0,0.2,0.4,0.6,0.8,1y=0,0.2,0.4,0.6,0.8,1

In fig. 3 shows the distribution of the electric field in various sections z=0,0.2,0.4,0.6,0.8,1z=0,0.2,0.4,0.6,0.8,1.It is seen that when moving away from the center of the coil, the lines of the electric field become circular.

In summary, the Induced Electric Field Lines near the square-shaped coil will be square-shaped near the coil and as we move away from the coil, the shape of these field lines will become circular.

I posted this question on Physics Stack Exchange and received the above response from Alex Trounev (works as a senior AI researcher at Likalo, LLC. He is one of the top 2% of the researchers in the world on Physics Stack Exchange).

The whole conversation can be found here.

What shape does the Induced Electric Field Lines take when in a region there is Non-Cylindrical… was originally published in Intuitive Physics on Medium, where people are continuing the conversation by highlighting and responding to this story.

Following is the Wein’s Displacement Law, in Thermal Radiations.

Following is the Distribution of Kinetic Energy of Beta Particles in Radioactive Decays.

Following is the distribution of Intelligence among people in general.

Following is the distribution of Salaries in various countries among people.

Do you notice a pattern here?

All of them are Bell-Shaped curves. All the graphs shown above come from completely different fields of studies and still, they share a similar distribution pattern. Isn’t it strange and amazing? Doesn’t that point to some hidden mysteries of nature?

The bell-shaped curve is a common feature of nature and psychology. In statistics it is called a “Normal Distribution” and it is given a lot of importance in statistics and probabilistic distributions.

What is a Normal Distribution in Statistics?

A normal distribution has a bell-shaped curve and is symmetrical around its center, so the right side of the center is a mirror image of the left side.

Most of the continuous data values in a normal distribution tend to cluster around the mean, and the further a value is from the mean, the less likely it is to occur. The tails are asymptotic, which means that they approach but never quite meet the horizon (i.e. x-axis).

For a perfectly normal distribution the mean, median and mode will be the same value, visually represented by the peak of the curve.

The normal distribution is often called the bell curve because the graph of its probability density looks like a bell. It is also known as called Gaussian distribution, after the German mathematician Carl Gauss who first described it.

Why is the normal distribution important?

The bell-shaped curve is a common feature of nature and psychology

The normal distribution is the most important probability distribution in statistics because many continuous data in nature and psychology displays this bell-shaped curve when compiled and graphed.

For example, if we randomly sampled 100 individuals we would expect to see a normal distribution frequency curve for many continuous variables, such as IQ, height, weight and blood pressure.

Parametric significance tests require a normal distribution of the samples’ data points. The most powerful (parametric) statistical tests used by psychologists require data to be normally distributed. If the data does not resemble a bell curve researchers may have to use a less powerful type of statistical test, called non-parametric statistics.

The normal distribution is so important in statistics that statisticians have written down books and have developed several theorems on just this single idea! One of the epitome of such theorems is Central Limit Theorem, which summarizes the idea discussed so far.

Later, I posted the same question on Physics Stack Exchange too, to receive more knowledge on the subject and yes it resulted positively. Following is the conversation.

https://physics.stackexchange.com/questions/521843/why-most-distribution-curves-are-bell-shaped-is-there-any-physical-law-that-lea

Further Readings and explorations.
1. The Normal Distribution: Crash Course Statistics #19
2. What is a Normal Distribution in Statistics?
3. Why is Normal Distribution Bell Shaped?
4. The Normal Distribution and the 68–95–99.7 Rule (5.2)
5. Why do airlines sell too many tickets? — Nina Klietsch

The Bell-Shaped Curve: A Common Pattern in Nature… was originally published in Intuitive Physics on Medium, where people are continuing the conversation by highlighting and responding to this story.

Around 1159 A.D., a mathematician called Bhaskara the Learned sketched a design for a wheel containing curved reservoirs of mercury. He reasoned that as the wheels spun, the mercury would flow to the bottom of each reservoir, leaving one side of the wheel perpetually heavier than the other. The imbalance would keep the wheel turning forever. Bhaskara’s drawing was one of the earliest designs for a perpetual motion machine, a device that can do work indefinitely without any external energy source. Imagine a windmill that produced the breeze it needed to keep rotating. Or a lightbulb whose glow provided its own electricity. These devices have captured many inventors’ imaginations because they could transform our relationship with energy. For example, if you could build a perpetual motion machine that included humans as part of its perfectly efficient system, it could sustain life indefinitely. There’s just one problem. They don’t work.

Ideas for perpetual motion machines all violate one or more fundamental laws of thermodynamics, the branch of physics that describes the relationship between different forms of energy.

The first law of thermodynamics says that energy can’t be created or destroyed. You can’t get out more energy than you put in. That rules out a useful perpetual motion machine right away because a machine could only ever produce as much energy as it consumed. There wouldn’t be any leftover to power a car or charge a phone.

But what if you just wanted the machine to keep itself moving? Inventors have proposed plenty of ideas. None of them work.

Even if engineers could somehow design a machine that didn’t violate the first law of thermodynamics, it still wouldn’t work in the real world because of the second law of thermodynamics. The second law of thermodynamics tells us that energy tends to spread out through processes like friction. Any real machine would have moving parts or interactions with air or liquid molecules that would generate tiny amounts of friction and heat, even in a vacuum. That heat is energy escaping, and it would keep leeching out, reducing the energy available to move the system itself until the machine inevitably stopped.

Various kinds of Perpetual Motion Machines can be classified in following categories and here we see, why they are doomed to fail given our current understanding of Science.

• A perpetual motion machine of the first kind produces work without the input of energy. It thus violates the first law of thermodynamics: the law of conservation of energy.
• A perpetual motion machine of the second kind is a machine which spontaneously converts thermal energy into mechanical work. When the thermal energy is equivalent to the work done, this does not violate the law of conservation of energy. However, it does violate the more subtle second law of thermodynamics (see also entropy). The signature of a perpetual motion machine of the second kind is that there is only one heat reservoir involved, which is being spontaneously cooled without involving a transfer of heat to a cooler reservoir. This conversion of heat into useful work, without any side effect, is impossible, according to the second law of thermodynamics.
• A perpetual motion machine of the third kind is usually (but not always) defined as one that completely eliminates friction and other dissipative forces, to maintain motion forever (due to its mass inertia). Such a machine should satisfy the following 3 properties, at the least.
  The machine should not have any “rubbing” parts: Any moving part must not touch other parts. This is because of friction that would be created between the two. This friction will ultimately cause the machine to lose its energy to heat.
  The machine must be operated inside a vacuum (no air): The reason for this has to do with the reason listed in number one. Operating the machine anywhere will cause the machine to lose energy due to the friction between the moving parts and air. Although the energy lost due to air friction is very small, remember, we are talking about perpetual motion machines here, if there is a loss mechanism, eventually, the machine will still lose its energy and run down (even if it takes a long, long time).
  The machine should not produce any sound: a Sound is also a form of energy; if the machine is making any sound, that means that it is also losing energy.
  It is impossible to make such a machine, as dissipation can never be completely eliminated in a mechanical system, no matter how close a system gets to this ideal.

So far, these two laws of thermodynamics have stymied every idea for perpetual motion and the dreams of perfectly efficient energy generation they imply. Yet it’s hard to conclusively say we’ll never discover a perpetual motion machine because there’s still so much we don’t understand about the universe. Perhaps we’ll find new exotic forms of matter that’ll force us to revisit the laws of thermodynamics. Or maybe there’s a perpetual motion on tiny quantum scales. What we can be reasonably sure about is that we’ll never stop looking. For now, the one thing that seems truly perpetual is our search.

Following are some popular proposals for Perpetual Motion Machines, which may seem convincing in the first sight, but on detailed analysis, they contradict at least one of the Laws of Thermodynamics.

There are concepts and technical drafts that propose “perpetual motion”, but on closer analysis, it is revealed that they actually “consume” some sort of natural resource or latent energy, such as the phase changes of water or other fluids or small natural temperature gradients, or simply cannot sustain the indefinite operation. In general, extracting work from these devices is impossible.

Resource consuming

Some examples of such devices include:

• The drinking bird toy functions using small ambient temperature gradients and evaporation. It runs until all water is evaporated.
• A capillary action-based water pump functions using small ambient temperature gradients and vapor pressure differences. With the “Capillary Bowl”, it was thought that the capillary action would keep the water flowing in the tube, but since the cohesion force that draws the liquid up the tube in the first place holds the droplet from releasing into the bowl, the flow is not perpetual.

• A Crookes radiometer consists of a partial vacuum glass container with a lightweight propeller moved by (light-induced) temperature gradients.
• Any device picking up minimal amounts of energy from the natural electromagnetic radiation around it, such as a solar-powered motor.
• Any device powered by changes in air pressure, such as some clocks (Cox’s timepiece, Beverly Clock). The motion leeches energy from moving air which in turn gained its energy from being acted on.
• The Atmos clock uses changes in the vapor pressure of ethyl chloride with temperature to wind the clock spring.
• A device powered by radioactive decay from an isotope with a relatively long half-life; such a device could plausibly operate for hundreds or thousands of years.
• The Oxford Electric Bell and Karpen Pile, driven by dry pile batteries.

Low friction

• In flywheel energy storage, “modern flywheels can have a zero-load rundown time measurable in years”.
• Once spun up, objects in the vacuum of space — stars, black holes, planets, moons, spin-stabilized satellites, etc. — dissipate energy very slowly, allowing them to spin for long periods. Tides on Earth are dissipating the gravitational energy of the Moon/Earth system at an average rate of about 3.75 terawatts.
• In certain quantum-mechanical systems (such as superfluidity and superconductivity), very low friction movement is possible. However, the motion stops when the system reaches an equilibrium state (e.g. all the liquid helium arrives at the same level.) Similarly, seemingly entropy-reversing effects like superfluids climbing the walls of containers operate by ordinary capillary action.

Thought experiments

In some cases, a thought experiment appears to suggest that perpetual motion may be possible through accepted and understood physical processes. However, in all cases, a flaw has been found when all of the relevant physics is considered. Examples include:

• Maxwell’s demon: This was originally proposed to show that the Second Law of Thermodynamics applied in the statistical sense only, by postulating a “demon” that could select energetic molecules and extract their energy. Subsequent analysis (and experiment) have shown there is no way to physically implement such a system that does not result in an overall increase in entropy.
• Brownian ratchet: In this thought experiment, one imagines a paddle wheel connected to a ratchet. Brownian motion would cause surrounding gas molecules to strike the paddles, but the ratchet would only allow it to turn in one direction. A more thorough analysis showed that when a physical ratchet was considered at this molecular scale, Brownian motion would also affect the ratchet and cause it to randomly fail to result in no net gain. Thus, the device would not violate the Laws of thermodynamics.
• Vacuum energy and zero-point energy: In order to explain effects such as virtual particles and the Casimir effect, many formulations of quantum physics include background energy which pervades empty space, known as vacuum or zero-point energy. The ability to harness zero-point energy for useful work is considered pseudoscience by the scientific community at large. Inventors have proposed various methods for extracting useful work from zero-point energy, but none have been found to be viable, no claims for extraction of zero-point energy have ever been validated by the scientific community, and there is no evidence that zero-point energy can be used in violation of conservation of energy.

References
1. Why don’t perpetual motion machines ever work? — Netta Schramm
2. Science Explained: The Physics of Perpetual Motion Machines
3. Perpetual Motion.

Perpetual Motion Machines — Why They Don’t Work? was originally published in Intuitive Physics on Medium, where people are continuing the conversation by highlighting and responding to this story.

“It is impossible for any heat engine to be more efficient than a Carnot engine when operating between two given temperatures”.

The Carnot engine is a conceptual engine that achieves the most efficient conversion of heat to work permitted by Kelvin’s statement. In general, efficiency is defined as the ratio of work out to heat in:

For a Carnot engine, the efficiency is found in terms of the temperature of the reservoirs the engine operates between:

Carnot’s Theorem

It is impossible for any heat engine to be more efficient than a Carnot engine when operating between two given temperatures:

Consider a heat engine drawing heat Q1 from a heat reservoir at temperature T1​, delivering work W and dumping heat Q2​ into a heat sink at temperature T2.

The heat engine operates in cycles, that is, it takes in heat Q1, does work W, dumps heat Q2, and in the end returns back to its original unchanged state.

Consider the net change in entropy ΔS of the universe:

The heat reservoir releases a heat Q1 at a constant temperature T1. Thus the change in its entropy is

The heat sink accepts heat Q2 at a constant temperature T2. Thus the change in its entropy is

Thus the net change in entropy of the universe is

Using the second law of thermodynamics, ΔS≥0, which implies

Since the left-hand side represents the efficiency of the given heat engine (η) and the right-hand side is the efficiency of a Carnot engine,

Hence proved!

Carnot Engine: Proof of Carnot Theorem... was originally published in Intuitive Physics on Medium, where people are continuing the conversation by highlighting and responding to this story.

What does the Equipartition theorem say about energy distribution?

In classical statistical mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition. The original idea of equipartition was that, in thermal equilibrium, energy is shared equally among all of its various forms; for example, the average kinetic energy per degree of freedom in the translational motion of a molecule should equal that in rotational motion.

I don’t know what “degree of freedom” means for instance.

So at relatively low temperatures, the energy of the molecules, (by hitting off of each other) will mean they eventually have the same amount of energy as they travel between the 3 different basic directions, Vx, Vy and Vz.

The energy gets shared equally, given enough time because no particular direction or no particular orientation or no particular degree of freedom has any special preference over the other.

As the temperature increases, they begin to rotate about their axis, the Vx, Vy and Vz axis. Except for diatomic molecules, like O2, which only have two axes of rotation.

Then as the temperature increases even more and the molecules bounce off of each other harder, the bonds between the atoms vibrate, like the tiny springs and masses of a harmonic oscillator.

Image Source: University of Manchester

This chart shows you how the temperature affects the way in which the internal energy of the system is divided.

The energy is distributed among all the degree of freedom equally because when millions of molecules are moving in a container randomly then there will be collisions of all the kinds among the molecules and no particular direction, or no particular orientation, or no particular degree of freedom, will have any special preference over the other, so statistically and probabilistically, it is safe to assume that energy will be same in all the degree of freedoms and if it is same then we can say the total energy will be distributed equally among all the degree of freedoms. When we assume the law of equipartition of energy then it leads to several results that match with the reality i.e. data collected in various other scientific experimentation. The predictions made by it are true, so it’s reasonable to assume “Equipartition of Energy”. It’s an assumption but it makes the right predictions.

Further Readings: Degree of Freedom: What is the need for this concept?

Law of Equipartition of Energy: Kinetic Theory of Gases. was originally published in Intuitive Physics on Medium, where people are continuing the conversation by highlighting and responding to this story.

We know that Temperature is the measure of Average Kinetic Energy of molecules of the gas. Greater is the temperature, greater is the average kinetic energy of the gas molecules. The kinetic energy of gas molecules can be due to several reasons. For example — If the gas molecule is diatomic then by the concepts of rotational dynamics, it can have translational kinetic energy, rotational kinetic energy and also vibrational kinetic energy. When average kinetic energies in all these dimensions are added together then we get the net total average kinetic energy of the molecule.

The next question which comes here is, why do we need to distribute the total kinetic energy of the molecule in various dimensions like translational, rotational and vibrational? Why can’t we just call it the net average kinetic energy?

The reason we need to distribute it is, “Law of Equipartition of Energy”. According to the Law of Equipartition of Energy, the total kinetic energy of a molecule is distributed equally, in all the independent number of ways it can possess kinetic energy, and the total number of independent ways in which a molecule can possess energy is called “Degree of Freedom”.

I will discuss the “Law of Equipartition of Energy” in the next article.

Next Article: The Law of Equipartition of Energy: Kinetic Theory of Gases.

Degree of Freedom. What is the need for this concept? was originally published in Intuitive Physics on Medium, where people are continuing the conversation by highlighting and responding to this story.

Aristotle‘s theory of gravity earlier stated that objects fall at speed proportional to their mass, which means the heavier the object is, the faster it will fall under gravity. Heavier object accelerates greater under gravity was believed to be true in Aristotle’s Time till Galileo conducted a thought experiment that disproved Aristotle’s assertion.

According to a biography by Galileo’s pupil Vincenzo Viviani, in 1589 the Italian scientist Galileo had dropped two balls of different masses from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass. Via this method, he supposedly discovered that the objects fell at the same acceleration independent of their masses. This was contrary to what Aristotle had taught: that heavy objects fall faster than lighter ones, in direct proportion to weight. While this story has been retold in popular accounts, there is no account by Galileo himself of such an experiment, and it is accepted by most historians that it was a thought experiment which did not actually take place.

Whether the experiment is conducted in real or not, the thought experiment actually proves that objects would fall with the same acceleration under gravity, independent of their masses.

Galileo arrived at his hypothesis by a famous thought experiment outlined in his book “On Motion”.

Following is the amazing thought experiment.

Let's assume that Heavier objects do Fall Faster than the Lighter ones.

Now, Imagine two objects, one light and one heavier than the other one, are connected to each other by a string. Drop this system of objects from the top of a tower. If we assume heavier objects do indeed fall faster than lighter ones (and conversely, lighter objects fall slower), the string will soon pull taut as the lighter object retards the fall of the heavier object, and thus the net acceleration of the system (lighter and heavier object together) will be less than the acceleration of heavier object alone! Which is actually a contradiction of the original assumption. The system (lighter and heavier object together) is heavier than the heavy body alone and thus should fall faster than the heavy body, but it is accelerating slower than a heavy body, which is a contradiction of the terms.

In this way, the assumption is proved to be false.

If we assume otherwise that lighter objects fall faster than the heavier objects then also we will reach the same contradiction by a similar argument.

It leaves us with only one possibility that objects fall with the same acceleration independent of their masses.

Hence Proved.

This thought experiment shows us the power of thought. It shows us that we can also find out about some real laws governing the universe without doing any physical experiments.

Galileo’s Leaning Tower of Pisa Thought Experiment: Acceleration due to gravity is independent of… was originally published in Intuitive Physics on Medium, where people are continuing the conversation by highlighting and responding to this story.

When lecturing about conservation of energy in the 1960s, Richard Feynman remarked:

It is important to realize that in physics today, we have no knowledge of what energy is. We do not have a picture that energy comes in little blobs of a definite amount. It is not that way. However, there are formulas for calculating some numerical quantity, and when we add it all together it gives “28” — always the same number. It is an abstract thing in that it does not tell us the mechanism or the reasons for the various formulas. [1]

Though it is tough to define an abstract concept like Energy, still following is a meager attempt.

Energy is any quantity — a number with the appropriate units (in the SI system, Joules) — that is conserved as the result of the fact that the laws of physics don’t depend on the time when phenomena occur, i.e. as a consequence of the time-translational symmetry. This definition, linked to Emmy Noether’s fundamental theorem, is the most universal among the accurate definitions of the concept of energy.

What is the “something”? One can say that it is a number with units, a dimensionful quantity. I can’t tell you that energy is a potato or another material object because it is not (although, when stored in the gasoline or any “fixed” material, the amount of energy is proportional to the amount of the material). However, when I define something like a number, it is actually a much more accurate and rigorous definition than any definition that would include potatoes. Numbers are much more well-defined and rigorous than potatoes which is why all of physics is based on mathematics and not on the cooking of potatoes.

Centuries ago, before people appreciated the fundamental role of maths in physics, they believed e.g. that the heat — a form of energy — was a material called the phlogiston. But, a long long time ago experiments were done to prove that such a picture was invalid. Einstein’s E=mc² partly revived the idea — energy is equivalent to mass — but even the mass in this formula has to be viewed as a number rather than something that is made out of pieces that can be “touched”.

Energy has many forms — terms contributing to the total energy — that are more “concrete” than the concept of energy itself. But the very strength of the concept of energy is that it is universal and not concrete: one may convert energy from one form to another. This multiplicity of forms doesn’t make the concept of energy ill-defined in any sense.

Following is what Richard Feynman says on Conservation of Energy.

There is a fact, or if you wish, a law, governing all natural phenomena that are known to date. There is no known exception to this law — it is exact so far as we know. The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same. (Something like the bishop on a red square, and after a number of moves — details unknown — it is still on some red square. It is a law of this nature.)

References:

1. What is Energy? Where did it come from?
2. Conservation of Energy by Richard Feynman.

What is Energy? was originally published in Intuitive Physics on Medium, where people are continuing the conversation by highlighting and responding to this story.