Re: [Phys-l] gas laws

["Robert Cohen" <Robert.Cohen@po-box.esu.edu>]

On Wednesday, February 15, 2006 11:20 PM, John Denker wrote:
> Here's an interesting exercise: Choose the best completion:
>    Other things being equal, for an ideal gas, ...
>       __
>      |__|  (A)  ... when the temperature goes up, the volume goes up,
>               and when the temperature goes down, the volume 
> goes down.
>       __
>      |__|  (B)  ... when the temperature goes up, the volume 
> goes down,
>               and vice versa.

I understand where you'd like to say "the answer depends on what other
things are being equal: entropy or pressure".  However, when I read this
exercise, I think that there is something causing the temperature to go
up.  That means that all other things cannot be equal.  Either we are
adding heat/increasing entropy (keeping the pressure constant) or we are
increasing the pressure (keeping the entropy constant).

I know this is your point, but to me, the way the problem is worded, it
implies that we change the temperature and, as a consequence, the volume
changes accordingly to maintain "other things being equal".  That
implies the first option (i.e., the temperature is changed by adding
heat while the pressure remains constant).

If, on the other hand, the exercise was worded
>    Other things being equal, for an ideal gas, ...
>       __
>      |__|  (A)  ... when the volume goes up, the temperature goes up
>               and when the volume goes down, the temperature
> goes down.
>       __
>      |__|  (B)  ... when the volume goes up, the temperature 
> goes down,
>               and vice versa.

the implication is that we are changing the volume and, as a
consequence, the temperature changes accordingly to maintain "other
things being equal".  That implies the second option (i.e., the volume
is changed by changing the pressure while the entropy remains constant).

Perhaps a better wording would be
>    Other things being equal, for the volume and temperature of an
ideal gas, ...
>       __
>      |__|  (A)  ... when one goes up, the other goes up
>               and when the one goes down, the other goes down.
>       __
>      |__|  (B)  ... when the one goes up, the other goes down,
>               and vice versa.
and then you can point out that we cannot have "all other things being
equal" but rather must make an assumption about how we are going to
cause one to go up or down.

So, in summary, if you use the first version, most people would say (A)
and I would agree (A) makes more sense (although you would say "it
depends").  If you use the second version, most people would probably
STILL say (A), although I would argue (B) makes more sense (and you
would still say "it depends").

____________________________________________________
Robert Cohen, Chair, Department of Physics
East Stroudsburg University; E. Stroudsburg, PA 18301
570-422-3428; www.esu.edu/~bbq