A few days ago, a good friend of mine (since by IITB-student days) wrote:
Among engineers, I believe Mechanical Engineers ("We", henceforth) live happily with entropy. We need it to analyse and design compressors, turbines, pumps, ejectors, mixers, ... .
We develop a feel for it.
Imagine our student (and for many, professional) life without an entropy axis (and it is always the x-axis, the major axis) on T-s, p-s, h-s, and so many other diagrams!
Even the good-old-professor B. B. Parulekar (of Khandu Patil fame) was happy to work with entropy, even though he kept away from the mathematics involved in its derivation.
And without entropy, we will find it difficult to define Gibbs Function, and hence chemical potential. How do we study chemical equilibrium without it?
Maybe 10% of students who study thermodynamics understand entropy fully.
To paraphrase Francis Bacon:
Some students just taste entropy, others just swallow it, and some few chew and digest it.
But fractions are confusing. When I started teaching (as a formal teacher at IIT Bombay), my first lectures on thermodynamics were to a group of some 42 UG students. But there was a core group of about 20 to 25 students (and they typically sat in a 5x5 or 4x6 formation, front, centre of the classroom, even their relative positions were almost fixed). These were the alert ones, trying to understand everything, and ready to jump at the teacher if anything went off-track or was confusing. I soon realised that I was teaching, essentially, these students. [The class size went from 42 to 60 to 90 to ..., but the number in the core group remained the same, more or less.]
And I think these were the students who understood entropy. And some of them continued to flirt with it, some had it as their girlfriend (half or otherwise), some are married to it and are living happily!
While discussing with Prof Achuthan on not-any-particular-topic (and this was common), we realised that there are perhaps three types of manipulations that we need to do.
From the simple to the not-so-simple, these are:
Numerical manipulation (NM):
Arithmetic++. All students are good at this. And with the advent of calculators, our effective ability at NM has improved significantly. Traditionally, active members of the trading class were excellent at NM. We continue to do, actually need to do, NM throughout our life.
Symbolic manipulation (SM):
Algebra++. A large majority of students are good at this. This begins in high school with algebra, then trigonometry and calculus, then calculus++. A large number of science and engineering graduates are good at SM. And, the advent of software for symbolic manipulation has improved our effective ability in SM. We keep on doing some sort of SM later in life. Scientists and engineers do it continuously throughout their professional life.
Concept manipulation (CM):
This is the ability to handle different concepts, and then fields, together. We have to do it, as students, to absorb high-level concepts in mathematics, science, and engineering. Later, only perhaps researchers and professors do it!
Remember our school/college/maybe even university exams?
Questions were usually chapter-wise. One chapter - one question (if at all). In geometry, each question was (a) some theorem to prove, and (b) a rider in which that theorem was the main idea needed. This requires a low level of CM, if at all.
But if you are confronted with a problem which requires material from two or more chapters from the textbook of a given subject, then you have to do a bit of conceptual manipulation, and this increases the degree of difficulty. Real-life situations need ideas and concepts from different fields. For example, detailed modelling of an electrical machine needs that we use electromagnetism, fluid mechanics, thermodynamics, heat transfer, as well as solid mechanics (to determine thermal stresses, and structural deformation). This needs a reasonable amount of concept manipulation.
Even in a given subject, we need to combine and extend concepts (terms, definitions) to create newer concepts.
In thermodynamics, the major concepts are energy, temperature, and entropy. Of these, energy straddles many (almost all) branches of physics, and is not very difficult to grasp. Temperature is a basic thermodynamic idea, and requires some concept manipulation, using the zeroth law of thermodynamics.
The idea of entropy involves a significant amount of concept manipulation. That is because it is (almost) the final extract of a derivation beginning with the second law of thermodynamics.
Just consider (this will be familiar to those who are still friends with entropy): We start with
the second law of thermodynamics - the Kelvin-Planck statement. Then we take a very scenic tour through heat engines, a definition of efficiency, thermal reservoirs, 2T-heat-engines, a hierarchy of temperature levels, a definition of 'higher' and 'lower' temperatures, (possibly a detour to refrigerators/heat-pumps, and their performance parameters,) the idea of reversibility and reversible processes, the Carnot theorem, the Carnot engine, thermodynamic temperature scales, thermodynamic Kelvin scale, (the Carnot cycle, and proof of equivalence of thermodynamic-Kelvin and ideal-gas-Kelvin scales,) the Clausius inequality and its proof; and then using the equality part of Clausius inequality we arrive at the definition of entropy. This requires a significant amount of algebraic as well as conceptual manipulation.
Another fact is that the ideas of energy ("the ability to do work") and temperature ("degree of hotness") are introduced in school, with very simplistic methods. One of my (self-assigned) tasks in IIT Bombay is to make our students get rid of (unlearn) many such ideas from their school days.
Unfortunately, for entropy, there is no 'short-and-sweet' definition (however incorrect). Hence, the belief that entropy is a dry, purely theoretical, and abstract concept!
We should also understand that many of the terms we use are short-forms (terminology). In thermodynamics, we use the word 'system' as a short form for 'a region of space, with well-defined boundaries, in which we are interested'. 'Property (of a system)' is a short form for 'relevant measurable characteristic (of a system)'. Imagine our frustration if we do not use such terminology during our study of thermodynamics (or for that matter, any science).
Unfortunately, for 'entropy', there is no 'expanded form'. It is an extraction of all that the second law of thermodynamics stands for.
That is what makes an appreciation of entropy difficult. I mentioned that maybe 10% of my students understand it. In professional life, even a smaller number need to use it. This small-usage fraction is true not just for entropy, it is true for a large number of topics and concepts, sometimes whole subjects! Any reader of this blog with an engineering and/or science background will appreciate this.
So, perhaps, the reasoning of the brother-and-niece was this: we did not use entropy in our professional life (and maybe we did not understand it as students), so it need not be taught.
Imagine implementing the same logic on X (replace X by your favourite concept) . If one takes this to its logical end, we will have to close down, maybe, our whole education system!
This morning me, my brother and niece (who are both chemical engineers) were discussing thermodynamics and in particular, entropy.
My brother and niece were convinced that entropy is a purely theoretical, abstract, and dry concept, and need not be taught.
I narrated our old story of ejector design in detail and how you helped with a revised analysis covering entropy (which was not considered in the original design), and how it worked perfectly well after that.
Since you have taught entropy in your teaching of thermodynamics many times, tell me, how many of your students really understand entropy?He wanted me to comment. So, here goes:
Among engineers, I believe Mechanical Engineers ("We", henceforth) live happily with entropy. We need it to analyse and design compressors, turbines, pumps, ejectors, mixers, ... .
We develop a feel for it.
Imagine our student (and for many, professional) life without an entropy axis (and it is always the x-axis, the major axis) on T-s, p-s, h-s, and so many other diagrams!
Even the good-old-professor B. B. Parulekar (of Khandu Patil fame) was happy to work with entropy, even though he kept away from the mathematics involved in its derivation.
And without entropy, we will find it difficult to define Gibbs Function, and hence chemical potential. How do we study chemical equilibrium without it?
Maybe 10% of students who study thermodynamics understand entropy fully.
To paraphrase Francis Bacon:
Some students just taste entropy, others just swallow it, and some few chew and digest it.
But fractions are confusing. When I started teaching (as a formal teacher at IIT Bombay), my first lectures on thermodynamics were to a group of some 42 UG students. But there was a core group of about 20 to 25 students (and they typically sat in a 5x5 or 4x6 formation, front, centre of the classroom, even their relative positions were almost fixed). These were the alert ones, trying to understand everything, and ready to jump at the teacher if anything went off-track or was confusing. I soon realised that I was teaching, essentially, these students. [The class size went from 42 to 60 to 90 to ..., but the number in the core group remained the same, more or less.]
And I think these were the students who understood entropy. And some of them continued to flirt with it, some had it as their girlfriend (half or otherwise), some are married to it and are living happily!
While discussing with Prof Achuthan on not-any-particular-topic (and this was common), we realised that there are perhaps three types of manipulations that we need to do.
From the simple to the not-so-simple, these are:
Numerical manipulation (NM):
Arithmetic++. All students are good at this. And with the advent of calculators, our effective ability at NM has improved significantly. Traditionally, active members of the trading class were excellent at NM. We continue to do, actually need to do, NM throughout our life.
Symbolic manipulation (SM):
Algebra++. A large majority of students are good at this. This begins in high school with algebra, then trigonometry and calculus, then calculus++. A large number of science and engineering graduates are good at SM. And, the advent of software for symbolic manipulation has improved our effective ability in SM. We keep on doing some sort of SM later in life. Scientists and engineers do it continuously throughout their professional life.
Concept manipulation (CM):
This is the ability to handle different concepts, and then fields, together. We have to do it, as students, to absorb high-level concepts in mathematics, science, and engineering. Later, only perhaps researchers and professors do it!
Remember our school/college/maybe even university exams?
Questions were usually chapter-wise. One chapter - one question (if at all). In geometry, each question was (a) some theorem to prove, and (b) a rider in which that theorem was the main idea needed. This requires a low level of CM, if at all.
But if you are confronted with a problem which requires material from two or more chapters from the textbook of a given subject, then you have to do a bit of conceptual manipulation, and this increases the degree of difficulty. Real-life situations need ideas and concepts from different fields. For example, detailed modelling of an electrical machine needs that we use electromagnetism, fluid mechanics, thermodynamics, heat transfer, as well as solid mechanics (to determine thermal stresses, and structural deformation). This needs a reasonable amount of concept manipulation.
Even in a given subject, we need to combine and extend concepts (terms, definitions) to create newer concepts.
In thermodynamics, the major concepts are energy, temperature, and entropy. Of these, energy straddles many (almost all) branches of physics, and is not very difficult to grasp. Temperature is a basic thermodynamic idea, and requires some concept manipulation, using the zeroth law of thermodynamics.
The idea of entropy involves a significant amount of concept manipulation. That is because it is (almost) the final extract of a derivation beginning with the second law of thermodynamics.
Just consider (this will be familiar to those who are still friends with entropy): We start with
the second law of thermodynamics - the Kelvin-Planck statement. Then we take a very scenic tour through heat engines, a definition of efficiency, thermal reservoirs, 2T-heat-engines, a hierarchy of temperature levels, a definition of 'higher' and 'lower' temperatures, (possibly a detour to refrigerators/heat-pumps, and their performance parameters,) the idea of reversibility and reversible processes, the Carnot theorem, the Carnot engine, thermodynamic temperature scales, thermodynamic Kelvin scale, (the Carnot cycle, and proof of equivalence of thermodynamic-Kelvin and ideal-gas-Kelvin scales,) the Clausius inequality and its proof; and then using the equality part of Clausius inequality we arrive at the definition of entropy. This requires a significant amount of algebraic as well as conceptual manipulation.
Another fact is that the ideas of energy ("the ability to do work") and temperature ("degree of hotness") are introduced in school, with very simplistic methods. One of my (self-assigned) tasks in IIT Bombay is to make our students get rid of (unlearn) many such ideas from their school days.
Unfortunately, for entropy, there is no 'short-and-sweet' definition (however incorrect). Hence, the belief that entropy is a dry, purely theoretical, and abstract concept!
We should also understand that many of the terms we use are short-forms (terminology). In thermodynamics, we use the word 'system' as a short form for 'a region of space, with well-defined boundaries, in which we are interested'. 'Property (of a system)' is a short form for 'relevant measurable characteristic (of a system)'. Imagine our frustration if we do not use such terminology during our study of thermodynamics (or for that matter, any science).
Unfortunately, for 'entropy', there is no 'expanded form'. It is an extraction of all that the second law of thermodynamics stands for.
That is what makes an appreciation of entropy difficult. I mentioned that maybe 10% of my students understand it. In professional life, even a smaller number need to use it. This small-usage fraction is true not just for entropy, it is true for a large number of topics and concepts, sometimes whole subjects! Any reader of this blog with an engineering and/or science background will appreciate this.
So, perhaps, the reasoning of the brother-and-niece was this: we did not use entropy in our professional life (and maybe we did not understand it as students), so it need not be taught.
Imagine implementing the same logic on X (replace X by your favourite concept) . If one takes this to its logical end, we will have to close down, maybe, our whole education system!
