AP Physics 1 2015 Free Response Question 3

Question: 
A block is initially stationary at position x = 0 and is in contact with a massless spring that is uncompressed. The block is then slowly compressed along a frictionless surface from position x = 0 to x = -D (See figure 1 below) such that ∆x = D. When the block is released, it reaches a rough part of the track at the right-hand side of x = 0 and it eventually slows down to rest at position x = 3D. Assume the coefficient of kinetic frictional force between the block and rough track is μ.

 

                                                                                 Fig. 1

In this question, students have to explain the correct and incorrect aspects of the following statement: “if the spring is compressed twice as long as before, the block has more energy when it leaves the spring, so it will slide farther along the track before stopping at position x = 6D.”

Scoring Guidelines:

Identify the correct aspect: the block has more energy when it leaves the spring.	1 point
Identify the incorrect aspect: the new final position of the block is not at x = 6D. (The spring’s elastic potential energy is proportional to the square of ∆x.)	1 point

(Source: http://apcentral.collegeboard.com/home)

Comments:

The main purpose of this question is to examine the relationship between the energy stored in a compressed spring-block system and the work done by the frictional (kinetic) force on the block after it leaves the spring. In other words, the question is about the transformation of the elastic potential energy of the block into its kinetic energy and thermal energy (microscopic internal energy). However, there are terminological and language issues in this question.

1. Terminological issues: It is surprising that the question and scoring guidelines adopt imprecise terminologies. For example, based on the scoring guideline for (b)(i), the student is correct because the block will have more energy when it leaves the spring. Note that the term “energy” could be changed to “kinetic energy.” To be more precise, it could be further changed to “translational kinetic energy” that is different from “rotational kinetic energy.” Next, based on the scoring guideline for (b)(ii), the student is incorrect because the spring’s energy does not scale linearly with its compression. However, the term “spring’s energy” could be changed to “elastic potential energy.” It is stated in AP 1: Algebra-Based Exam Description that, “Essential knowledge 4.C.1: The energy of a system includes its kinetic energy, potential energy, and microscopic internal energy. Examples should include gravitational potential energy, elastic potential energy, and kinetic energy.”

2. Language issues: The sentence “the block will have more energy when it leaves the spring” in the question is misleading. Firstly, it seems to suggest that the block will have more energy, and thus violating the conservation of energy. More importantly, one may expect the block to be in contact with the spring until the spring is no longer compressed. Thus, after the block leaves the spring, the block’s (kinetic) energy starts to decrease at a constant rate because of frictional force of the track. This contradicts the statement that “the block will have more energy when it leaves the spring.” Perhaps the scoring guidelines could recognize students who identify the incorrect reasoning pertaining to “the block will have more energy when it leaves the spring”? Or perhaps the sentence could be rephrased as “the block will have relatively more kinetic energy when there is an increase in the compression of the spring”?

Feynman’s insights or goofs?:
The question adopts the term “spring’s energy” instead of “elastic potential energy.” In Feynman’s words, “[e]lastic energy is the formula for a spring when it is stretched. How much energy is it? If we let go, the elastic energy, as the spring passes through the equilibrium point, is converted to kinetic energy and it goes back and forth between compressing or stretching the spring and kinetic energy of motion. There is also some gravitational energy going in and out, but we can do this experiment ‘sideways’ if we like (Feynman et al., 1963, section 4–4 Other forms of energy).” That is, the motion of a spring may involve elastic energy, kinetic energy, and gravitational energy. However, physics teachers can use the following terms that are more precise: elastic potential energy, translational kinetic energy, and gravitational potential energy.

On the other hand, this question assumes that the frictional force is constant. Conversely, Feynman explains that “the frictional drag on a ball or a bubble or anything that is moving slowly through a viscous liquid like honey, is proportional to the velocity, but for motion so fast that the fluid swirls around (honey does not but water and air do) then the drag becomes more nearly proportional to the square of the velocity (Feynman et al., 1963, section 12-2 Friction).” Furthermore, Feynman states that “the drag force on an airplane is approximately a constant times the square of the velocity, or F ≈ cv² (Feynman et al., 1963, section 12-2 Friction).” However, the drag force can also be approximated by F ≈ av + bv². Importantly, Feynman clarifies that “as we study this law of the drag on an airplane more and more closely, we find out that it is ‘falser’ and ‘falser’ (Feynman et al., 1963, section 12-2 Friction).”

Interestingly, Feynman does not mention that the frictional force is independent of contact area which can be found in many physics textbooks. He explains that when there is good contact between two solids, they can hold very tight together and thus have a larger frictional force. Most important, Feynman adds that “to a fairly good approximation, the frictional force is proportional to this normal force, and has a more or less constant coefficient; that is, F = μN, where μ is called the coefficient of friction. Although this coefficient is not exactly constant, the formula is a good empirical rule for judging approximately the amount of force that will be needed in certain practical or engineering circumstances. If the normal force or the speed of motion gets too big, the law fails because of the excessive heat generated. It is important to realize that each of these empirical laws has its limitations, beyond which it does not really work (Feynman et al., 1963, section 12-2 Friction).”

Note:

1. Feynman also explains that “[i]n experiments of the type described above, the friction is nearly independent of the velocity. Many people believe that the friction to be overcome to get something started (static friction) exceeds the force required to keep it sliding (sliding friction), but with dry metals, it is very hard to show any difference (Feynman et al., 1963, section 12-2 Friction).” 

2. Jonathan Thomas-Palmer, for example, strongly disagrees with the use of the symbol K for the kinetic energy of the block because k stands for spring constant in the same question. (Source: https://www.youtube.com/watch?v=6dlijzUQHw4)

3. For another discussion of this question, you can visit the following websites:

https://www.youtube.com/watch?v=qQM-IGnxi6g
https://www.youtube.com/watch?v=KH60uz5LNWk

Reference: 

Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.

AP Physics 1 2015 Free Response Question 2

Question: 

Students are expected to describe an experimental procedure that could be used to answer the following question: “do fewer electrons leave a light bulb than enter the bulb in one second?” Next, they have to explain how experimental data can be used to answer the abovementioned question. (Assume that students are provided with voltmeters that are marked in 0.1 V increments and ammeters that are marked in 0.01 A increments.)

Scoring Guidelines:

Describe an analytical method of using experimental data and explain how the data can be used to answer the abovementioned question. Example: If the electric current measured is the same on both sides of the light bulb, then the number of electrons entering the bulb is the same as those leaving the bulb in one second.

1 point

(Source: http://apcentral.collegeboard.com/home)

Comments: 
In this question, students are expected to have a good concept of series circuits. The main purpose of the question is to assess students’ knowledge of experimental design and their ability in data analysis by using ammeters and voltmeters. Students were also asked to account the uncertainty of electrical measurement and to discuss how it affects the experimental results.

In the first part of this question, two ammeters are connected in series on both sides of the bulb to measure the electric current entering and leaving the bulb (based on the scoring guidelines). Importantly, we should not conclude that “the number of electrons per second entering and leaving the bulb is the same” if the electric current is measured to be the same on both sides of the bulb. There are both theoretical and experimental issues in this question. 

1. Theoretical issues: If the electric current through the ammeters on both sides of the bulb are the same, then the student expects the number of electrons per second entering and leaving the bulb are the same. This is based on a “simplified” definition of electric current: the number of electrons per second. However, to quote Feynman, “[e]lectric currents are electrons or other charges in motion with a net drift or flow (Feynman et al., 1964, section 13-2 Electric current; the conservation of charge).” Firstly, the electric current could be contributed by a flow of positive charge carriers such as copper atoms in the wire, but they are “almost essentially” stationary. Secondly, the magnitude of electric current is also dependent on the drift velocity of electrons. Thus, the electric current is not simply the number of electrons per second moving through the bulb.

2. Experimental issues: In this question, the ammeters are marked in 0.01 A increments. However, one may prefer to use clamp meters which have 0.001 A resolution and they do not introduce additional electrical resistance. More importantly, if the uncertainty in measuring an electric current is 0.01 A, this may imply a possible error of 0.01 C in one second. Therefore, the uncertainty in measurement corresponding to the number of electrons per second could be of the order 10¹⁷ because the electric charge of an electron is 6.02 × 10^-19 C. In a sense, this experiment is analogous to the use of a meter ruler to conclude that the atoms and electrons have the same length. From an empiricist’s perspective, one should not comment about the number of electrons per second entering and leaving the bulb are the same when there are limitations (or significant uncertainty) in measuring the electric current accurately.

Currently, an ampere is defined as the electric current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these two conductors a magnetic force that is equal to 2 × 10^–7 N/m. In other words, the ampere is not defined as one electron at a particular time based on current technology. Furthermore, the definition of an ampere in terms of two infinitely long conductors cannot be precisely implemented in practice. Recently, Dr. Giblin (2016) and researchers from National Physical Laboratory’s Quantum Detection Group and the University of Cambridge have reported the counting of electrons trapped in an electron pump (a small region of a specially designed semiconductor device) with a fidelity of one part per million. Thus, the electron pump could be the new primary reference standard of electric current. However, there are still significant errors in counting the number of electrons.

Feynman’s insights or goofs?:

Feynman states that “[e]lectric currents are electrons or other charges in motion with a net drift or flow (Feynman et al., 1964, section 13–2 Electric current; the conservation of charge).” In other words, an electric current is a net drift or flow of charge carriers such as electrons. However, Feynman’s definition of the electric current can be improved. For example, physics teachers may prefer to define the electric current as the time rate of flow of charge carriers. That is, we can distinguish the rate of flow with respect to time from the rate of flow with respect to displacement. Furthermore, the electric current can be more comprehensively defined as the rate of flow of ‘free’ electrons (or other charge carriers) per unit time due to a potential difference across the ends of an electrical conductor, under constant circuit conditions.

On the other hand, some physicists advocate the use of operational definitions. However, Feynman did not provide an operational definition of electric current. For example, Karplus (2003) writes that: “Operational definition: Electric current is measured by the dial reading of a standard ammeter (p. 315).” Furthermore, an ampere is defined as the electric current that can produce an attractive force of 2 × 10⁻⁷ N per meter of length  between two straight, parallel conductors of infinite length placed one meter apart in a vacuum. Importantly, a problem of the operational definition of electric current is that an uncertainty of 0.01 ampere in measuring an electric current corresponds to an uncertainty of 10¹⁷ electrons per second. Note that this operational definition is a measure of an effect of electric current that is a magnetic force.

Interestingly, Feynman has an insightful explanation on the effects of electric current: “[w]e ask what happens in a piece of resistance wire when it is carrying a current. Since the wire has resistance, there is an electric field along it, driving the current. Because there is a potential drop along the wire, there is also an electric field just outside the wire, parallel to the surface. There is, in addition, a magnetic field which goes around the wire because of the current. The E and B are at right angles; therefore there is a Poynting vector directed radially inward, as shown in the figure. There is a flow of energy into the wire all around. It is, of course, equal to the energy being lost in the wire in the form of heat. So our “crazy” theory says that the electrons are getting their energy to generate heat because of the energy flowing into the wire from the field outside. Intuition would seem to tell us that the electrons get their energy from being pushed along the wire, so the energy should be flowing down (or up) along the wire. But the theory says that the electrons are really being pushed by an electric field, which has come from some charges very far away, and that the electrons get their energy for generating heat from these fields (Feynman et al., 1964, section 27-5 Examples of energy flow).”

Note:
1. You may want to visit this website:

http://feynman-answer.blogspot.sg/2016/08/electric-current-flow-of-electrons-or.html

2. For another discussion of this question, you can visit the following website:
https://www.youtube.com/watch?v=OpbYvr8yhqQ

References:

1. Feynman, R. P., Leighton, R. B., & Sands, M. L. (1964). The Feynman Lectures on Physics, Vol II: Mainly electromagnetism and matter. Reading, MA: Addison-Wesley. 

2. Giblin, S. P., See, P., Petrie, A., Janssen, T. J. B. M., Farrer, I., Griffiths, J. P., ... & Kataoka, M. (2016). High-resolution error detection in the capture process of a single-electron pump. Applied Physics Letters, 108(2), 023502.
3. Karplus, R. (2003). Introductory physics: A Model approach (2nd ed.). Buzzards Bay: Captain’s Engineering Services.

AP Physics 1 2015 Free Response Question 1

Question: 
This question is based on a simple Atwood’s machine: two blocks are connected by a massless string passing over massless pulleys which are frictionless (See figure 1 below). Block 2’s mass (m₂) is greater than block 1’s mass (m₁). Students have to derive the magnitude of the acceleration of block 2 when the two blocks are released from rest. The answer should be expressed in terms of m₁, m₂, and g.

Fig. 1

It could be of interest to mention that a similar question can be found in Feynman’s Tips on Physics. The question involves the calculation of frictional force: “Two masses, m₁ = 4 kg and m₃ = 2 kg, are connected with cords of negligible weight over essentially frictionless pulleys to a third mass, m₂ = 2 kg. The mass m₂ moves on a long table with a coefficient of friction…(Feynman et al., 2006, p. 144).”

Scoring Guidelines:

Using Newton’s second law for block 1 m1a = T – m1g	1 point
Using Newton’s second law for block 2 m2a = m2g – T	1 point
Eliminate T and derive the acceleration: T = m1a + m1g m2a = m2g – m1a – m1g (m2 + m1)a = (m2 – m1)g a = (m2 – m1)g / (m1 + m2)	1 point

(Source: http://apcentral.collegeboard.com/home)

Comments:

The main purpose of the question is to assess students’ ability to apply Newton’s second law of motion to a modified Atwood’s machine. Students are expected to have a basic knowledge of free body diagrams and an understanding of factors that determine the acceleration of the system. However, they may have difficulty with the use of conventions for force and acceleration because one block is moving upward and the other block is moving downward.

We may expect this question to be simply answered by using Newton’s Second law of motion as shown below:

To find the acceleration of block 2, we can visualize an “equivalent question” in which the forces acting on block 1 and block 2 are shown in figure 2 below: Fig. 2 The larger force, m2g, acting on block 2 is the driving force and the smaller force, m1g, acting on block 1 is the opposing force. For block 2: the driving force (m2g) is in the direction to the right, whereas the tension (T) is in the direction to the left. By using Newton’s Second Law of motion, ΣF = ma we have m2g – T = m2a ------ (1) (Convention: The forces that are in the direction to the right are assigned positive.) For Block 1: The tension (T) is in the direction to the right and the opposing force (m1g) is in the direction to the left. By using Newton’s Second Law again, we have T – m1g = m1a ------(2) By solving the two equations (1) and (2), a = (m2 – m1)g / (m1 + m2) However, we can visualize block 1 and block 2 as a system. In this case, the total mass is m1 + m2 and the external forces on the system are m2g – m1g. Thus, a = F/m = (m2 – m1)g / (m1 + m2) Would students be penalized by using only one equation?

Feynman's insights?:
Alternatively, Feynman explains that “the laws of Newton could be stated not in the form F = ma but in the form: the average kinetic energy less the average potential energy is as little as possible for the path of an object going from one point to another (Feynman et al., 1964, section 19–1 A special lecture—almost verbatim).” That is, it is possible to use Euler-Lagrange’s equation to answer this question. Interestingly, Mr. Bader introduced the principle of least action to his student, Feynman. In addition, Dias, Araújo, Silva, Santos, Barros, & Carvalho-Santos (2012), for example, propose to introduce Euler-Lagrange’s equation in introductory physics. However, it is unclear whether students who use a more advanced method could be awarded extra credit or penalized instead. (I happen to know of a high school student who was able to apply Euler-Lagrange’s equation to solve mechanics problems that are even more difficult.)

It is not difficult to use Euler-Lagrange’s equation to solve this question on Atwood’s machine. It can be accomplished by using only a few steps as shown below: 
The kinetic energy of the system (T) is given by T = ½ m₁ẋ² + ½ m₂ẋ² 

The potential energy of the system (U) is given by U = – m₂gx – m₁g(l – x) 

Thus, the Lagrangian can be written as 

T – U = ½m₁ẋ² + ½m₂ẋ² + m₂gx + m₁g(l – x)

By using Euler-Lagrange’s equation of motion, d/dt(∂L/∂ẋ) – ∂L/∂x = 0

We get (m₁ + m₂)ẍ – (m₂ – m₁)g = 0

Therefore, ẍ = (m₂ – m₁)g/(m₁ + m₂)

(Would some physics teachers penalize students for using Euler-Lagrange’s equation to get the correct answer?)

Note:
1. In Feynman’s words, “when I was in high school, my physics teacher—whose name was Mr. Bader—called me down one day after physics class and said, ‘You look bored; I want to tell you something interesting.’ Then he told me something which I found absolutely fascinating, and have, since then, always found fascinating. Every time the subject comes up, I work on it. In fact, when I began to prepare this lecture I found myself making more analyses on the thing. Instead of worrying about the lecture, I got involved in a new problem. The subject is this—the principle of least action (Feynman et al., 1964, section 19–1 A special lecture—almost verbatim).”

2. For another discussion of this question, you can visit the following websites:
https://www.youtube.com/watch?v=NrNG6OPijeY
https://www.youtube.com/watch?v=ff6SNrgUFt0

References:
1. Dias, C. F., Araújo, M. A., Silva, G. M., Santos, C. A., Barros Jr, P., & Carvalho-Santos, V. L. (2012). Adaptation of the Euler-Lagrange equation for studying one-dimensional motions in a constant force. arXiv preprint arXiv:1209.2197.

2. Feynman, R. P., Gottlieb, M. A., Leighton, R. (2006). Feynman's tips on physics: reflections, advice, insights, practice: a problem-solving supplement to the Feynman lectures on physics. San Francisco: Pearson Addison-Wesley.

3. Feynman, R. P., Leighton, R. B., & Sands, M. L. (1964). The Feynman Lectures on Physics, Vol II: Mainly electromagnetism and matter. Reading, MA: Addison-Wesley.

IB Physics 2015 Higher level Paper 2 Question 7

Question: Diffracted electrons through a thin layer of graphite are incident on a fluorescent layer. Students are expected to explain how an observable pattern demonstrates that electrons have wave properties.

Mark Scheme: 
(1) bright and dark rings / circles / circular fringes. 
(2) maximum and minimum / constructive and destructive. 
(3) mention of interference / mention of superposition. 
(4) link to interference being characteristic of waves.

Comments:

Based on the mark scheme, students are expected to state circular fringes (or similar descriptions) and link the observable pattern to a characteristic of waves. That is, they have to specify the observable pattern when electrons are incident on a fluorescent layer in the tube. As a suggestion, students could mention that “bright and dark rings or circular fringes could be observed at the end of the tube.” The bright rings (or circular fringes) are due to constructive interference, whereas dark rings are due to destructive interference. Importantly, the circular fringes can be linked to the wave-like properties of electrons instead of particle-like properties.

Furthermore, students could explain that “the circular fringes are a result of interference (or superposition) which is a wave-like property of electrons.” That is, the formation of fringes follows the principle of superposition because electrons behave like waves. However, interference is not the only characteristic of a wave. For example, Knight (2004) suggests that wave properties could be described as non-localized, continuous, and collective (Knight, 2004). On the other hand, in Hertz’s experiment, “[t]he waves were found to exhibit the properties of: 1. reflection; 2. refraction; 3. interference; 4. diffraction; 5. polarization; and 6. they travelled at c (the speed of light) (Warren, 2003, p. 108).”

However, in Physics for the IB diploma, it is stated that: “when an electron moves inside a crystal whose interatomic spacing has similar dimensions as the de Broglie wavelength will diffraction take place (Tsokos’s 2008, p. 395).” That is, wave-like properties of electrons may include “diffraction” and “de Broglie wavelength.” Thus, students could specify that “the de Broglie wavelength of the diffracted electrons is dependent on their speeds and it should have similar dimensions as the interatomic spacing.” It is worth mentioning that the circular fringes occur where the path difference of the electron waves from the sources is zero or they differ by an integral multiple of the de Broglie wavelength.

Feynman insights?:

Interestingly, Feynman mentions that “[i]f we take these neutrons and let them into a long block of graphite, the neutrons diffuse and work their way along. They diffuse because they are bounced by the atoms, but strictly, in the wave theory, they are bounced by the atoms because of diffraction from the crystal planes (Feynman et al., 1963, section 38–3 Crystal diffraction).” In essence, diffraction is an important wave property of neutrons when they move inside a block of graphite. However, it is the slowest neutrons that pass through the long block of graphite. These neutrons have longer wavelengths and behave more like waves.

Importantly, Feynman explains that “[n]o one has ever been able to define the difference between interference and diffraction satisfactorily. It is just a question of usage, and there is no specific, important physical difference between them. The best we can do, roughly speaking, is to say that when there are only a few sources, say two, interfering, then the result is usually called interference, but if there is a large number of them, it seems that the word diffraction is more often used. So, we shall not worry about whether it is interference or diffraction (Feynman et al., 1963, section 30–1 The resultant amplitude due to n equal oscillators).” In short, there is diffraction in the phenomenon “interference,” and there is interference in the phenomenon “diffraction.” In other words, interference involves diffraction or spreadings of waves, whereas diffraction involves interference or summings of waves.

In addition, Feynman clarifies that “[h]istorically, the electron, for example, was thought to behave like a particle, and then it was found that in many respects it behaved like a wave. So it really behaves like neither (Feynman et al. 1963, section 37–1 Atomic mechanics).” Simply phrased, the electrons are neither particles nor waves. More importantly, Feynman elaborates that “[t]he electrons arrive in lumps, like particles, and the probability of arrival of these lumps is distributed like the distribution of intensity of a wave. It is in this sense that an electron behaves sometimes like a particle and sometimes like a wave (Feynman et al., 1963, section 37–5 The interference of electron waves).” In short, it is the distribution of electrons that is guided by a wave function or a probability wave. Moreover, electrons could be observed to have particle-like properties or wave-like properties depending on the experimental set-up.

Note:

In a sense, the phrase “wave properties” in the question should be changed to “wave-like properties.” For example, in Feynman’s own words, “the particle has wavelike properties (Feynman et al., 1966, section 3-1 The laws for combining amplitudes).”

References:

1. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.

2. Feynman, R. P., Leighton, R. B., & Sands, M. L. (1966). The Feynman Lectures on Physics, Vol III: Quantum mechanics. Reading, MA: Addison-Wesley.

3. Knight, R. D. (2004). Physics for Scientists and Engineers with Modern Physics. California: Addison-Wesley.

4. Tsokos, K. A. (2008). Physics for the IB diploma (5th ed.). Cambridge: Cambridge University Press.

5. Warren, N. (2003). Excel HSC Physics. Glebe, NSW: Pascal.

IB Physics 2015 Higher level Paper 2 Question 6

Question: Students are expected to provide a definition of the enhanced greenhouse effect. 

Mark Scheme: addition of greenhouse gases / named greenhouse gas to the atmosphere; increasing the temperature of Earth’s surface / global warming. 

Comments: 

In Physics for the IB diploma, the enhanced greenhouse effect is defined as “the additional warming of the caused by increased quantities of greenhouses gases. The increase in the greenhouse gas concentrations is mainly due to human activity (Tsokos, 2008, p. 824).” In a sense, the mark scheme is better than the textbook definition because it specifies the effect more clearly. That is, the mark scheme includes “increasing the temperature of the Earth’s surface,” whereas the textbook definition only mentions “additional warming.” On the other hand, the textbook definition states that “the increase in the greenhouse gas concentrations is mainly due to human activity.” However, this fact is not found in the mark scheme.

Importantly, the mark scheme and textbook definition of enhanced greenhouse effect can still be improved. For example, they could specify greenhouse gases such as carbon dioxide and methane. Furthermore, the mark scheme and textbook definition could clarify that the increase in the greenhouse gas concentrations can be due to human activities such as burning fossil fuels and agricultural farming. Conversely, Freeman Dyson, for example, opines that good scientists should be skeptical of the global warming. However, the majority of climate scientists believe that the global warming is “very likely” caused by human greenhouse gas emissions. Currently, there are different physical models on the enhanced greenhouse effect.

Feynman insights?:

One simple model to understand the distribution of various gases on the Earth is to assume we have a column of gas extending to a great height at thermal equilibrium, as well as without winds and other kinds of disturbance. Based on this model, Feynman explains that “if we have different kinds of molecules with different masses, they go down with different exponentials. The ones which were heavier would decrease with altitude faster than the light ones. Therefore, we would expect that because oxygen is heavier than nitrogen, as we go higher and higher in an atmosphere with nitrogen and oxygen the proportion of nitrogen would increase. This does not really happen in our own atmosphere, at least at reasonable heights, because there is so much agitation which mixes the gases back together again. It is not an isothermal atmosphere. Nevertheless, there is a tendency for lighter materials, like hydrogen, to dominate at very great heights in the atmosphere, because the lowest masses continue to exist, while the other exponentials have all died out (Feynman et al., 1963, section 40–1 The exponential atmosphere).” Essentially, the densities of various gases in earth’s atmosphere decrease exponentially with height based on the assumption of constant temperature and constant gravitational field.

Furthermore, Feynman elaborates how water vapors radiate heat to the sky. In his own word, “when you go up in altitude the air is colder. The ground is heated by the sun, and the re-radiation of heat to the sky comes from water vapor high in the atmosphere; so at high altitudes, the air is cold — very cold — whereas lower down it is warm. You may say, “Then it’s very simple. Warm air is lighter than cold; therefore the combination is mechanically unstable and the warm air rises.” Of course, if the temperature is different at different heights, the air is unstable thermodynamically. Left to itself infinitely long, the air would all come to the same temperature. But it is not left to itself; the sun is always shining (during the day). So the problem is indeed not one of thermodynamic equilibrium, but of mechanical equilibrium (Feynman et al., 1964, section 9–4 Thunderstorms).” That is, a realistic model of earth’s atmosphere for greenhouse effect cannot be based on thermodynamic equilibrium.

Note:

Physicists prefer to define heat as a process rather than a noun (Romer, 2001; Wong, Chu, & Yap, 2014). Thus, it is good to avoid phrases such as “heat-trapping gases” or “too much heat is trapped on Earth.”

References:

1. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley. 

2. Feynman, R. P., Leighton, R. B., & Sands, M. (1964). The Feynman Lectures on Physics, Vol II: Mainly electromagnetism and matter. Reading, MA: Addison-Wesley. 

3. Romer, R. H. (2001). Heat is not a noun. American Journal of Physics, 69(2), 107-109. 

4. Tsokos, K. A. (2008). Physics for the IB diploma (5th ed.). Cambridge: Cambridge University Press. 

5. Wong, C. L., Chu, H. E., & Yap, K. C. (2014). Developing a Framework for analyzing definitions: A Study of The Feynman Lecture. International Journal of Science Education, 36(15), 2481-2513.