How Does Compressing a Syringe Affect an Ideal Gas?

[adam878787878]

Homework Statement

if you have an ideal gas in a syinge, then you compress the syringe to a point, then that means that Volume has decreased. Consequentally, Pressure must increase to compensate (oin order for PV=nRT to be true) right?
I think this is wrong but I am not undersnating why..
please help ! thanks

Homework Equations

The Attempt at a Solution

 

[G01]

Think of it like this. Pressure is caused by molecules of the gas hitting the sides of the container. So, if you decrease the volume of the container, the gas molecules will have no choice but to hit the walls more often. Thus, if pressure is caused by molecules hitting off the walls, the pressure must increase is the molecules are hitting the wall more. This is why the pressure of a gas will increase if you decrease the volume of its container.

Does this make sense?

 

[adam878787878]

well, this homework questions says: "explain why the following statement is incorrect"...

"in the ideal gas law, P=nRt/V, so the pressure is inversely proportional to the volume. If you decrease the volume, the pressure has to go up"

That looks pretty correct to me! so i am stumped

 

[G01]

Hmmm. Yeah, that is the ideal gas law, and the ideal gas law is correct! I'm lost. Maybe ask your instructor about it. It seems to me that the question is either stated incorrectly, or we are missing part of it.

 

[adam878787878]

it ends by asking "What is the flaw in the student's reasoning?"

so the statement is wrong in someway, and I quoted it verbatim from the book.
any ideas?

 

[G01]

Ahh. I think I see the catch here!

Yes, when we decrease the volume, something must change to keep the equation true, but does this change have to be in the pressure? What other quantity in the ideal gas law is not always fixed?

 

[kdv]

well, this homework questions says: "explain why the following statement is incorrect"...

"in the ideal gas law, P=nRt/V, so the pressure is inversely proportional to the volume. If you decrease the volume, the pressure has to go up"

That looks pretty correct to me! so i am stumped

The problem is the "... the pressure has to go up..."

It does not necessarily have to go up and if it does go up, it does not have to go up like one over the volume.

 

[adam878787878]

ah ok i see.
n is not fixed also (so, could halve the gas and halve volume then pressure would stay same.)
thanks!

 

[stewartcs]

ah ok i see.
n is not fixed also (so, could halve the gas and halve volume then pressure would stay same.)
thanks!

There are only three state variables in the Ideal Gas Law, N is not one of them.

The statement in the book is correct only if you add the constraint of the temperature being held constant (Isothermal).

CS

 

[adam878787878]

isnt n moles of the gas? If you let 1/2 the gas escape, and half the volume, then P would stay same right?
if you can't change moles of gas, then how many moles of gas in ideal gas?
?

 

[stewartcs]

isnt n moles of the gas? If you let 1/2 the gas escape, and half the volume, then P would stay same right?
if you can't change moles of gas, then how many moles of gas in ideal gas?
?

The original question you posed asks about a cylinder being depressed (a syringe). It is implied that the gas cannot escape (or at least it seems that way to me), hence the number of moles is constant. The only variables are the pressure, volume (of the cylinder or syringe in this case), and the temperature. I believe the point they want you to understand is that the temperature may also be varied which would result in a pressure change also.

CS

 

[adam878787878]

i have another ideal gas law question.
how can we say that a mole of any ideal gas will "occupy" 22.4L , when by definition of ideal gas, they don't occupy any space?

 

[physixguru]

think about this and ur doubts will be cleared..if the space occupied by molecules of a ideal gas is negligible in comparison to the total volume then ..the p vs v graph of experimental data and that calculated by boyle's law should coincide.

THIS IS NOT THE CASE...

 

[stewartcs]

i have another ideal gas law question.
how can we say that a mole of any ideal gas will "occupy" 22.4L , when by definition of ideal gas, they don't occupy any space?

I'm not sure what you mean by an ideal gas being defined as to not occupy space.

Here is some more information on the Ideal Gas Law that may be of some help.

An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly eleastic and in which there are no intermolecular attractive forces. One can visualize it as a collection of perfectly hard spheres which collide but which otherwise do not interact with each other. In such a gas, all the internal energy is in the form of kinetic energy and any change in internal energy is accompanied by a change in temperature.

Source: http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/idegas.html#c4

CS