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Name: Lynda B.
Status: educator
Age: 40s
Location: N/A
Country: N/A
Date: 11/6/2004


Question:
We are currently discussing the Ideal Gas Law and Charles' Law. Using the example of a balloon being heated results in a larger volume, is very intuitive, and students have no difficulty grasping the concept. One student then said, well then if you increase the volume the temperature must increase. I told them, yes it would have to - the math tells us...but they are looking for something more tangible to relate to. Do you have a better explanation that can describe why the temp. should increase if the volume increases? Charles Law states : V1/T1 = V2/T2. Therefore an increase in temperature will increase the volume (balloon on a hot summer day). Another way to look at it is that if you increase the volume, the temperature must increase - this is harder to explain to students. Would you use the angle that the act of increasing the volume increases the kinetic energy of the molecules thus increasing the temperature?


Replies:
When explaining the gas laws it is necessary to be precise about specifying not only the units of the measurements but also the conditions of the changes. The "normal" unit of pressure (P) is atmospheres, of volume (V) is liters, of temperature(T) is kelvins, of amount of gas (n) is mols. In those units the gas constant, R=0.08205 liter-atm/mol-K and the defining ideal gas equation is: P*V = n*R*T. In the special case of Charles' law, the quantity of gas and the pressure of the gas are constant resulting in V1/T1 = V2/T2 or V2 = V1*(T2/T1). It is possible to change the temperature of the gas (holding the pressure and amount of gas constant) by adding or removing heat from the gas. This is an isobaric change. There is no way to carry out the process you describe, that is increasing the volume independent of heating it (increasing the temperature). For Charles' law to apply, if you start with a given volume V1 the only way to get to V2 is to heat the gas, thus increasing the temperature by a fixed ratio (T2/T1). The kinetic theory of gases shows that the kinetic energy of the gas depends ONLY on the temperature. So whatever you do to the gas, if you do not change the temperature, you do not change its energy. If you expand the gas from V1 to V2 without heating it (called and adiabatic expansion) the temperature of the gas will decrease, but the pressure also will not remain fixed.

Vince Calder


Lynda,

Preface: Charles / Boyles gas laws should really be taught all at the same time and be shown, within the same lecture (day) that they can be combined to form the COMBINED GAS LAW EQUATION and ultimately lead to the Ideal Gas Law equation of PV = nRT.

Well, this one is a tad bit of a play on words. V1 / T1 = V2 / T2 is very true. This equation needs to be treated with an understanding that the "path" is important. State 1 is V1 and T1, and likewise for State 2. But which came first, the chicken or the egg?

Your student's CHANGE OF STATE (VOLUME) is very path dependent. In other words...

We both know that the Volume (in this case) IS CAUSAL of the Temperature. Your very inquisitive student must realize that when he or she magically, or mathematically rather, increases the volume of the balloon the above equation should turn into the ideal gas equation PV = nRT ==> T = PV / nR. ==> V = nRT / P. You MAY NOT just "increase volume" without;

1.) Pulling on the balloon ( in all directions ) with some sort of sticky tape. This may distort the balloon into a larger volume. BUT the above equation shows that this course of action necessitates that the pressure, P, drop accordingly. CAUSE AND EFFECT.

OR

2.) You can "add" n moles of molecules of gas (air, etc...). However, this still means that you have "changed" the system by adding molecules. V1 / T2 = V2 / T2 NOW becomes an equation that no longer fully describes what is going on.

You asked, "Would you use the angle that the act of increasing the volume increases the kinetic energy of the molecules thus increasing the temperature?" The answer is No. I would reverse it, because the Temperature (heat added to the system) is the perturbation that CAUSEs your INCREASE in VOLUME. Not the other way around. It IS the increased molecular motion ( increasing T ) that causes the increase in V, volume.

The point of Charle's Law was to show that the ISOBARIC (constant pressure) change of the state variables T and V showed their PROPORTIONAL relationship. T goes up ==> V goes up. (ALL OTHER VARIABLES HELD CONSTANT) The point of Boyle's Law was to show that the ISOTHERMAL (constant temperature) change of the state variables P and V showed their INVERSELY PROPORTIONAL relationship. P goes up ==> V goes down. (all else held constant)

I hope that I have helped some. If not, please email us back.

Thank you,
Darin Wagner


Lynda,

You present an interesting case where theory tells us something should happen, but there is not a good real life example to demonstrate the principle. I admire your students for thinking outside the box.

I agree with your statements. Keep in mind that in your example, when you compare volume and temperature, you are keeping pressure constant. If you change the volume, the temperature must increase to maintain constant pressure. Unfortunately, what typically happens when you increase the volume is you reduce the pressure while maintaining constant temperature.

In your balloon example, increasing the temperature actually increases the pressure in the balloon. The air pressure in the balloon was balanced with the elasticity force of the balloon which wants to contract. The temperature change increases the internal pressure which then rebalances the forces by expanding the balloon.

Bob Hartwell


Rather than approach this from KMT or Thermodynamics which is going to be more confusing than illuminating for your students (and you could appear to be giving a hand-waving answer), I suggest this approach:

1) Remind them that Charles's Law works only if everything else (P, n) are held constant.

2) Increasing the volume (perhaps by pulling on the moveable wall of a cylinder) would have the effect of decreasing the internal pressure (Boyle's Law).

3) But that is not allowed under Charles's Law - so in order to maintain P constant, what do you have to do? Heat it up.

I find that this reasoning is more satisfying to the students (and I have college students), rather than bringing up Thermodynamics which they have not learned at this point. Hope it helps you.

Greg (Roberto Gregorius)



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