And they're PAID for this?

[Tor]

I've been helping someone who is looking at taking a GED (a test that gives a equivalent to a high school diploma), and found this question in the test prep book:

It is well known that the boiling point of water is 100 degrees Celsius. More viscous, or thicker, substances often have higher boiling points. Glycerin, for example, boils at 290 degrees Celsius, while olive oil boils at 300 degrees Celsius.

By what percentage is the boiling point of glycerin greater than that of water?

Now, there is nothing per se wrong with this, until you get to their answer:

190 According to the paragraph, glycerin's boiling point is 190 degrees greater than water's boiling point. To find the percentage by which glycerin's boiling point is greater than that of water, divide the difference between the two substances' boiling points by the boiling point of water and multiply the quotient by 100%. Thus, 190/100*100%=190%. Always read questions carefully. Glycerin's boiling point is 290% of water's boiling point, but this question asks for the percent by which glycerin's boiling point is greater than water's.

If highlighting that doesn't show the problem, then try this description:

The problem is that zero Centipede is not a real zero, but one arbitrarily defined so as to provide convenient numbers for everyday use. To picture the problem, take nine objects and put them in a pile, and to the right of it place six objects. Now separate three items from each pile just below the original pile. The space is equivalent to zero Celsius. Though with our arbitrary zero (that saves no end of headache in everyday use), the left pile now looks to contain twice as many objects as the first, but that forgets the other three items in each pile below our arbitrary zero. In reality, in our example, the left pile is but half again the right pile.

This is exactly the mistake made, and one that ordinary people can be forgiven for making, but (IMO, at least) it is the job of people writing this sort of thing to know enough to either include the complete information and make it right or declare it too complex and discard the question. In this case, when I looked at the question (hidden) I immediately tried to remember the Kelven offset from Celsius to answer it properly. The only thing that would have saved me from a "wrong" answer in a real test would have been that it would have been multiple choice - and doubtless not included the true correct answer as an option.

[Jim]

Yes, that was foolish.

I have taken some science classes and been a home school teacher. The test prep people should have hired someone with the similar qualifications to write their book.

[Big and Bashful]

To get an accurate answer they should have specified kelvin, at least that is measured from absolute zero. To be accurate they would also have to define the ambient pressure to get accurate boiling points for each fluid. Bad question.
If it is an elementary level question then I could understand the gross simplifications, a lot of teaching seems to be telling lies to children, to help them 'understand'. Then when you go to college, you are told to forget a lot of what you had been told at school because a lot of school teaching is either a simplification, inaccurate or just plain wrong.

The example I remember was the school I was at stating that a solid cannot be compressed. Become an apprentice, go to college, learn about poisson's ratio, i.e. how much a solid compresses when you squidge it a lot. Realise that school was not fantastic.
On the other side, my school did prepare me for the wonderful world of different number bases, e.g. binary, octal etc, they even covered simple calculus, but I am still not brilliant at calculusizing!

[Kirbstone]

Well, B&B, Ye've got to learn to integrate before you can differentiate!

Tom

[Big and Bashful]

I've never been very well integrated, always been a bit of an outsider!

[Tor]

To get an accurate answer they should have specified kelvin, at least that is measured from absolute zero.

Indeed - and that conversion is exactly what I started to try the moment I read the problem, but I only remembered the conversion truncated to the nearest degree. It /might/ be excusable if it were the math section, but this section is /supposed/ to be teaching about states of matter. Leaving out minor variables that scarcely change in everyday usage, like your mentioned pressure (in this case "sea level" pressure is a reasonable unstated assumption), is one thing. Making a percentage comparison based on a false zero is another matter altogether. I suppose making people believe things like this could help convince them that a gas heated by a solid can then further warm said solid -- if probably a rather unfair accusation that ends up leveled against some lackey in the bowels of some near dungeon somewhere, who is certainly not guilty of making any such attempt.

[crfriend]

Leaving out minor variables that scarcely change in everyday usage, like your mentioned pressure (in this case "sea level" pressure is a reasonable unstated assumption), is one thing.

I may still have the volume, but I recall one wonderful page in a book on physics entitled, "When is a 2 minute egg not a 2 minute egg?" and the topic was based entirely about the boiling point of water at assorted altitudes at which people actually live. If one looks at it, the boiling point of water up in the Andes is a fair bit lower than it is, say, in Death Valley in the USA. So, pressure does matter.

Making a percentage comparison based on a false zero is another matter altogether.

"Zero" is where somebody felt like putting it, and in so doing renders the entire thing rather arbitrary. Zero Fahrenheit was arbitrarily set by a chap (who named the scale, by the way) who went out one day with his newfangled mercury-containing gadget and commented, "Well, this is about as cold as it gets around here so I'll call it zero." Zero Celsius is just about as arbitrary, albeit better specified, as it refers to the freezing point of (distilled) water at one atmosphere ("sea level" -- try working that one over any sort of distance). Zero Kelvin is where molecular motion stops, but there's nothing to say that it cannot get colder than that, just that given the current state of the art we cannot measure anything below that point.

When I looked at the "question" I immediately took it as a "trick" and dismissed it as irrelevant. "Trick questions" can be useful for ferretting out thought patterns but really have no place on "standard tests".

I suppose making people believe things like this could help convince them that a gas heated by a solid can then further warm said solid [...]

This comes down to equilibrium, and things of differing masses, densities, and thermal capacities have different behaviours, but, in general, if something is being "cooled" something else is being "heated" and vice-versa. TANSTAAFL. ("There Ain't No Such Thing As A Free Lunch.") The remaining question can be boiled down to, "Is entropy increasing or decreasing?" and I'll leave that one for the cosmologists to debate. The notion of a gas being heated by a solid which is also heated is ludicrous on the face of it.

[Jack Williams]

This is highly interesting, but the light blue "highlighting" is impossible to read against the yellow. Perhaps red would be better.

[Tor]

Jack, the intent was not to highlight, but rather to allow the curious to think about the question and attempt answering it themselves without having a hard time avoiding reading the answer. Try highlighting the text when you wish to view it.

Carl, yes I am aware of the lowered boiling point of water at commonly inhabited elevated locations even on this globe - a phenomenon that taken further is the principle freeze drying is based upon. Perhaps I did discount that more than I ought. And yes, even "sea level" pressure varies a decent amount, especially if one permits the pressure of large storms to dictate the lower bound. Spacial variation in this can be anything ranging from a nuisance to a hazard for pilots (the latter really only for the unwary, though real enough. I've read a story of someone who nearly crashed into a mountain because of this.)

Though the situation I posed is ludicrous, I worded it so as to make the idiocy of it patently obvious. Sadly, it has in fact been put forth in a slightly less obvious form by folk who should be respectable. Some who are alert enough to catch them at it ascribe all manner of motivation behind their doing so. Equilibrium, of course, reigns as it must, however much some wishful thinkers would have otherwise.

[Jim]

"Zero" is where somebody felt like putting it, and in so doing renders the entire thing rather arbitrary. Zero Fahrenheit was arbitrarily set by a chap (who named the scale, by the way) who went out one day with his newfangled mercury-containing gadget and commented, "Well, this is about as cold as it gets around here so I'll call it zero."

I heard a slightly different story. 0°F was based on the temperature of an equal mixture of water, ice, and salt, the lowest Daniel Fahrenheit could produce in his lab. It was then designed to have an even 180° between freezing and boiling.

[Big and Bashful]

Jim,
That is how I heard it, I vote for your origin...

[crfriend]

0°F was based on the temperature of an equal mixture of water, ice, and salt, the lowest Daniel Fahrenheit could produce in his lab. It was then designed to have an even 180° between freezing and boiling.

That's equally possible, and would produce a somewhat reproducible sample point for calibrating the original instruments -- but, it's still an arbitrary point on a very wide scale. 180 degrees between (unsalted freezing and boiling)? I smell the Babylonians at work here -- just as they gave us the system of time that we use today (24/12:60:60) as well as angular measurements (360/60/60).

[Milfmog]

"Zero" is where somebody felt like putting it, and in so doing renders the entire thing rather arbitrary. Zero Fahrenheit was arbitrarily set by a chap (who named the scale, by the way) who went out one day with his newfangled mercury-containing gadget and commented, "Well, this is about as cold as it gets around here so I'll call it zero."

I heard a slightly different story. 0°F was based on the temperature of an equal mixture of water, ice, and salt, the lowest Daniel Fahrenheit could produce in his lab. It was then designed to have an even 180° between freezing and boiling.

The version of the story I heard placed zero as described but placed the 100 degree mark at human body temperature. Used that to mark the initial thermometer and divided the scale between into 100 increments. unfortunately the measured body temperature proved not to be accurate.

Of course, that could all be an old wife's tale... (Wikipedia not withstanding)

Have fun,


Ian.