Unruled Notebook

Entries from April 2007

Oh I see

April 26, 2007 · 6 Comments

The high school physics text books that I have studied usually devote a chapter for each of the different “branches” of physics. Perhaps not to scare the gentle (layman?) students off by using scary jargons, these chapters would be titled in “plain English” as, say, Light, Sound, Heat, Modern Physics (as against Optics, Acoustics etc.). In my home town high school public exam the question paper usually reserves disproportionate marks to the respective branches of physics above – more for Light and very less for Sound, for instance. The PJ before the exam is, “Study Light soundly and Sound lightly”.

There could be a sound point to this that should be apparent before the end of this post, but let me now digress into some thing Light.

Some time back, while preparing his Layman studies Light post Selva asked me by email this question, “Is it correct to say that we are able to see anything at all because light bends around the atoms and molecules in the air? The air is full of atoms that if light did not bend around them, we’d have a hard time seeing anything. Is this thought scientifically tenable or have I gone horribly wrong somewhere in my understanding?”

An explanation I mustered, which I present here with some modifications…

We “see” (say, each other) undisturbed by the air because it has very less density in a given volume to influence the light (so that it could obstruct light’s path by its molecules). So light doesn’t have to “bend around” the atoms. It more or less evades hitting them as there are only a few of them with a relatively large mean free path.

On the other hand, if we have the same light passing through a liquid, the molecules of that liquid do influence the light path and results in refraction. As you know, a measure of how much refraction happens is done through the refractive index of that medium (for air it is one).

On the other hand, even in air, say, inside a room where the two of us face each other and we keep “seeing” each other without any disturbance from the room air and its molecules, it is worth noting we also don’t see the dust that is present in the air (which is much bigger in size that the molecules of air) between us. The dust does actually reflect back the light but since the density of the dust again is relatively small in a room full of air, we still are able to “see” each other unhindered – if we are hindered, we will also see the dust particles.

Again, the density of the dust alone is not the controlling factor, but the intensity of the incident light also matters. As the sunlight using which we see each other in the room, in the first place, is of less intensity it doesn’t trigger the light sensitive part of the eye to discern the weak intensity variation in the reflected light from the dust particles. However, as we know, if we shine a torch (flash) light in the room, the column of the light beam has enough intensity to get scattered from the dust particles and reach our eyes with enough intensity for us to “see” the dust.

Again, in the same room if we use a laser beam, we should be able to see the dust.

There ends the explanation I wrote then. There is a thought that such explanations done mostly in “plain talk” are suited for the “layman (and woman)” and that is the best way to propagate Science. In my opinion there are no “laymen (or women)” in this World.

There are perhaps only (sound) explanations and light/lay-explanations, like the one given above.

UPDATE (addressing comments below):

1) Yes, refractive index of air is not EXACTLY EQUAL to 1, but in the context of this essay it is alright to �assume� it to be one.

2) Sunlight IS of less intensity when it reaches Earth surface. In fact, it IS diffuse radiation, the reason why we do all those solar �collecting� to (re)focus the sunlight.

On the other hand, the energy in sunlight when it comes out of the Sun IS definitely huge. But the intensity (total radiation per unit area) when it hits the Earth�s surface, in the visible spectrum, is about 600 kW/m^2 (again, this number is not exact, but not totally wrong either, I guess). Point is, when we see each other (visible spectrum) in a room lit ONLY by sunlight (from the windows, say), we don�t see the dust in between because sunlight gets reflected not only from the dust (which anyway is minimal) but also from other sources (us, table, chair, walls etc.) as well. The human eye is unable to discern the difference in the intensity of the reflected radiation from the dust over the rest of the reflection (OK, at least in the case of dust, ideally, I should replace reflection by scattering and there are three types of it etc., but I hope readers will allow me to use this terminology to keep the discussion simple).

On the other hand, light from a torch light close to its source (near the torchlight) IS of higher intensity than that of the sunlight that we have on Earth in the visible spectrum. Intensity also follows the inverse square law with distance right? So, in a room when a torch light is shined, I can see the dust particles near to the light source more because, the eye can discern the scattered light from the dust (which is of higher intensity as it is merely reflecting the high intensity light near to the source) more easily than that of the rest of the surrounding light. Of course, this works only with a small volume of space close to the source of the light.

Even in case of sunlight, if we make our high school pin-hole camera like set-up, the sunlight passing through the slit would be more localized to reflect from the dust, to be seen by us (if the rest of the room is assumed to be dark).

To tie this with what Lakshmi writes below in the comments, torch light, close to its source, has more photon density (more photons per unit volume) than at a far away distance. Same with Sunlight. A more intense radiation like that from a LASER would have less diffusion of their photons for relatively a long distance, hence their �intensity� is intact. Hence they will be reflected (scattered) by the dust also, with more intensity (when compared to the other light sources).

Categories: Science Notes · Thermal Sciences
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Research Evaluation

April 20, 2007 · 4 Comments

ommachi is the screen name I used at ToonDoo to create this strip

Categories: Academics · Cartoons
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How to quickly cool a bottle of drink using seven equations

April 16, 2007 · 16 Comments

Say, you have your favorite drink in a bottle (water, in my case, beer for most of my friends and coke for most of my students) with dimensions of axial length about 5 times that of the diameter. You want to drink it cold (at a reasonably less than room temperature). If you are given the choice of putting the bottle inside a refrigerator to cool it, how (on Earth) will you place the bottle full of drink so that it cools faster: horizontally or vertically (see Fig. 1)?

bottleinfridge.PNG

Figure 1

Treating the bottle full of drink as a thermodynamic closed system (one which doesn’t allow Mass to escape out or get in, but allows the same with Energy) one can readily see, if the bottle needs to be cooled, it needs to release its energy out to the environment (refrigerator in this case, which is assumed to be at a lesser temperature) so that it cools (temperature, the representation of how much internal energy there is in the bottle, is lowered). And the objective is to do this as quickly as possible.

Writing First Law of Thermodynamics for the “closed” bottle “system”

  \frac{dE}{dt} = -Q_{drink \rightarrow air} \cdots (1)

where E is the internal energy of the bottle of drink and the equation indicates per second how much of that is expelled out as heat Q into the surrounding (refrigerated) air. Since we don’t have a meter that measures directly this E and Q, we resort to simplifying Eq. (1) into some measurable quantities, leading us to

  (mc)_{drink} \cdot \frac{dT_{drink}}{dt} = -hA(T_{drink} - T_{air}) \cdots (2)

where ‘mc’ is the thermal capacity of the drink in the bottle, ‘h’ the convection heat transfer coefficient and ‘A’ is the surface area of the bottle across which the convection of heat from the drink to the air takes place. That means, A is the bottle surface area “wetted” by the surrounding air on the outside and by the drink on the inside (assuming negligible thickness for the bottle wall).

To find the time required to cool the drink from its initial highest temperature T_drink to any lower temperature, one could rearrange suitably Eq. (2) into a “variable separable” form and simply integrate the resulting equation to arrive at the necessary solution. Doing so, would result in an equation similar to

  t\sim\frac{(mc)_{drink}}{hA} \cdots (3)

Of course, one can arrive to Eq. (3) from Eq. (2) by scaling arguments, if one recognizes that the time it takes for the drink to cool from its original temperature T_drink to the final possible temperature of T_air is the maximum possible one, which can be found as Eq. (3), by setting the dT_drink as equal to the (T_drink – T_air) in Eq. (2).

An interesting thing to observe form Eq. (3) is that except for the ‘h’ the rest of the quantities (such as m, c and A) can be safely assumed not to vary with the orientation of the drink bottle (will this assumption ever fail?). This means the time taken for the drink in the bottle to cool is simply inversely proportional to the convection heat transfer coefficient – higher the ‘h’, the quicker the drink cools.

Several ways of enhancing the ‘h’ exist and can be basically differentiated through what type of convection situation one ends up with namely, natural or forced (free or paid). For instance, in our situation, it is intuitively obvious for us if we blow over the bottle (forced convection), we could cool it faster than when it is required to cool by itself (natural convection).

Unfortunately, we don’t expect ourselves to sit inside our fridge and keep blowing over the bottle, so it is alright to assume that the bottle be allowed to cool by natural convection mode of heat transfer.

Since we are given the choice of two positions (see Fig. 1), it is safe to assume that the natural convection heat transfer coefficient would depend on the position of the bottle (else we have no problem at hand). Therefore one can write for the two positions given in Fig. 1

  \frac{t_1}{t_2} = \frac{h_2}{h_1} \cdots (4)

All that now remains is to estimate the overall heat transfer coefficient by some means. In principle the overall ‘h’ is a combination of the heat transfer coefficients of both the drink and the air, as both offer resistance for the energy to get transferred as heat from the drink to the air. For the sake of brevity of this post, let us take it for granted that

  h_{drink} \gg h_{air} \cdots (5)

(This is true anyway for most of the drinks including coke and beer [1]. For water, h_water is about 60 times larger than h_air at 10 degree C).

In other words, the overall ‘h’ in Eq. (4) is controlled more by h_air and so if one finds that out, it can be safely substituted into Eq. (4) to find the answer for the cooling time.

Now from research carried out so far and well documented in text books of convection heat transfer [1], one can learn that the natural convection heat transfer coefficient ‘h’ depends on the Rayleigh Number of the configuration in the following way

  h\sim h_{air}\sim\frac{1}{H}\cdot \left(kRa_H^{\phantom{H}1/4}\right)_{air} = (\textrm {constant})\cdot H^{-1/4} \cdots (6)

(‘k’ is the thermal conductivity of air, which is treated as a constant). For a given temperature difference between the drink and the air, and known thermo-physical properties of air (density, kinematic viscosity, coefficient of thermal expansion), this means, the ‘h’ simply is inversely proportional to the height H of the configuration (the drink bottle, in our case) that is undergoing the natural convection cooling.

Using this Eq. (6) into Eq. (4) along with the fact that H1 is five times that of H2 (as given in Fig. 1), it is obvious that

  \frac{t_1}{t_2} = \frac{h_2}{h_1} = \left( \frac{H_1}{H_2} \right) ^{1/4} = 5^{1/4} = 1.50 \cdots (7)

This means the time required to cool in the vertical position (position 1 in Fig. 1) for the drink bottle is 50 % LONGER than that required when the bottle is kept in horizontal position (position 2 in Fig. 2) inside the refrigerator.

Chill that drink quickly by placing it horizontally inside the fridge.

Note

There are assumptions made here that could cause doubts. Assumption of natural convection as the only mode of heat transfer is one. But as explained at the start, it can be safely considered to be the only dominant mode of heat transfer in this situation. Heat transfer from the bottle walls in contact with the fridge surface etc. is minimal. Same way, assuming the bottle as a cylinder, neglecting the geometrical variation near the neck is also fine. We are not concerned with the exact time or heat transferred in Watts. We need only a comparison estimate between two positions and in both instances the bottle is assumed with similar geometry. There are others that are not discussed here.

If you don’t believe the equations here (as one engineer reader wrote to me), just take two identical bottles of water and put one in the door-side vertical slot and the other on the horizontal tray in a standard fridge and do the experiment and check the results. If you can find two small bottles that can fit into the freezer cabinet upright (vertically), you can reach this cool result even quicker.

Reference

[1] Convection Heat Transfer by A. Bejan, in which the above situation is given as an end of the chapter exercise.

Categories: Lecture Notes · Science Notes · Thermal Sciences
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Five Minutes on Open Science

April 11, 2007 · 7 Comments

As some of my students and colleagues are aware, I advocate strongly about doing science as openly as possible in all of its evolving steps including the gestation of the idea, method(s) to solve/answer, reporting of the results along with original data and sustenance of progress related to those results through open dialogs. Of course, a nice place to do that is online.

Here is a video of an engaging talk by my friend Deepak on Open Science at Ignite Seattle. Deepak sums up nicely within five minutes, all of the angles I have mentioned above.

One of the major drawbacks of open science is the seeming lack of incentive and recognition that it generates when viewed through the existing, possibly myopic, academic evaluation process that deems a scientist to be successful or not. In my opinion, the only way open science can flourish is to make the academic evaluation process (used for promotion, peer recognition, research funding etc.) more accommodative and include “open sciencing ” as a necessary component for evaluating academic excellence and success.

I do have some potentially inflammatory ideas on how to do this, but this post is just to whet your appetite and reflect on the possibilities of Open Science. More discussions will follow in this blog soon.

Categories: Academics
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Notes on Owning a Domain and Moving WordPress

April 9, 2007 · 11 Comments

Its been a while since Nonoscience moved to its own domain. This post is to answer two related questions from readers and friends.

1) Why have a domain and pay for it, while a million free blog offering sites are available?

My perceived advantages

  1. Freedom. I am recalcitrant and learn more if left to myself. I need to slosh and gulp and gasp for breath to learn my swimming. And in the process if I get to die, so be it. So much so that a free blog site is a dent in my bloatocratic ego.
  2. Learning. Web page development I learnt by trial and (more) error. So did I about blogging and related software, including PHP and MySQL. So when I registered my domain an year back, I did it with a conscious motive of learning as an avocation all of these stuff. The science blog grew more as a side effect.
  3. Control. Your own domain gives you more of this. Instead of the user interface (dashboard) alone, you get to see and use the back end (actual files and database). This helps at times of trouble…
  4. …and it seems having your own domain and blog saves you from getting caught in the generic blog blackouts that happen whimsically in democratic India.

I should add to this that, contrary to perceived belief among some bloggers, hosting and domain charges are not that expensive. If un povero professore like me can do it, why not others?

There should be many other advantages that could be cited, which I leave for the appropriate readers to fill in the comments.

2) How to move wordpress blog from own domain to another?

Again, there are perhaps more than a GB of free information online (and growing everyday) about how to do this. My megalomaniac take on this is of course, don’t bother to read all of the detailed steps given here there and everywhere on how to do this and how things could go wrong. Things will go wrong anyway and even after following all of the instructions to the tee.

Advice1: Find your own (better) way of doing the move.

Advice 2: The way that worked for me in a matter of minutes is to

  • simply download the entire database from the old domain,
  • open it as a text file in say, wordpad and
  • by using the “find and replace” option change the instances of old address (in my case, http://unrulednotebook.wordpress.com) to the new domain address (http://unrulednotebook.wordpress.com) and
  • save the file
  • upload this file as the new database in the new domain
  • Of course, wordpress needs to be installed successfully at the new domain before taking the above steps.
  • Finally, copy the entire contents of the “wp-content” folder from the old blog to the new one. This folder would contain themes, plugins, uploads etc.

Now I am pitching for a dedicated server for Nonoscience DOT Info with my hosting service. Will share the easier way on how to do this, once I learn it by doing all the mistakes.

And finally, the disclaimer (what with there are humans here who put their cat in the microwave and chose to sue the manufacturer because specific instructions to the contrary hasn’t been provided…):

I may be wrong in all of the above so don’t take my word for it. Try the above suggestions at you own risk.

Meanwhile, off to post some representative stuff for the blog…

Tags: wordpress, own domain, dreamhost, web hosting, moving wordpress blogs

Categories: Information
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