[mike316]

Hi
Today on our test we had a multiple choice question and I think it had 2 answers. I emailed the professor and he says he disagrees. I want your opinion.

The question was something like "which one of the following is true about ideal gases?"
choice A said temperature and average speed are directly related.
choice C said pressure is caused by particles colliding with the walls of the container.

I think temperature and average speed are directly related, are they not?
I emailed the prof and he said Average speed is NOT directly related to temp., kinetic energy is directly related not speed.

but if you look at the equation Vrms=sqrt(T/M), to me, this equation indicates that average speed and temperature are directly related.

Do you agree that choice A is also correct?

[Borek]

Direct proportion usually means linear relation, so

[tex]E=\frac 1 2 kT[/tex]

is a direct proportion, while

[tex]v=\sqrt{\frac{kT}{m}}[/tex]

is not.

At least that'd how I would understand it, but English is my second language,

[fledarmus]

Borek is exactly right - the kinetic energy is directly related to temperature, while the velocity is directly related to the square root of the temperature.

"directly related" (also known as "directly proportional", or using "varies directly with") has a very specific meaning in math (at least in English) - y is directly related to x if and only if there is a non-zero constant k such that  y = kx

[mike316]

Borek is exactly right - the kinetic energy is directly related to temperature, while the velocity is directly related to the square root of the temperature.

"directly related" (also known as "directly proportional", or using "varies directly with") has a very specific meaning in math (at least in English) - y is directly related to x if and only if there is a non-zero constant k such that  y = kx

well, wikipedia disagrees with both of you
"In mathematics and statistics, a positive or direct relationship is a relationship between two variables in which change in one variable is associated with a change in the other variable in the same direction."

[Borek]

You asked for an opinion, you got it. Using wikipedia in such discussions is not the best idea, wikipedia is not the ultimate source.

This is mostly semantics - does "directly related" and "directly proportional" mean the same? We say no, you say yes. Your best line of defense is that the wording of the answer is ambiguous - but I don't think it is.

[fledarmus]

Please link your source. Although your statement is true, it is only part of the definition. If you like Wikipedia, you might try this page instead...

http://en.wikipedia.org/wiki/Directly_proportional and read down to the section labeled "direct proportionality"

[Borek]

http://en.wikipedia.org/wiki/Direct_relationship

[fledarmus]

Ahhh, the author of that link is making a distinction between a "direct relationship" and a "direct linear relationship". I'm afraid you will have to go to a mathematics forum to argue that point. My understanding has always been that a direct relationship is by definition linear; you wouldn't say "y is directly related to x" if you meant that y varied proportionately with the square root of x; instead you would say "y is directly related to the square root of x".

If you search "direct relationship" in enough places and can find a sufficiently authoritative source that not all direct relationships are linear, that may be enough to convince your grader. It would have been enough to convince me if I was still teaching.