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## 30 January 2012

### How to justify an answer: Equations, Calculations, or Facts

One mole of an ideal gas expands from a volume of 5 L to a volume of 10 L at atmospheric pressure.  Does the gas's temperature increase, decrease, or remain the the same?  Justify your answer.

Justifications are tough for novice physics students, especially students with weak verbal skills.  Look at some common unacceptable responses to the question above:

* Increase, because the volume increased at constant pressure.  [This answer is a tautology -- it simply restates information given in the problem.]

* Increase, because the temperature had to go up to increase the volume.  [Still a tautology.  "Had to" doesn't add any physics understanding.]

If we're not vigilant about scanning justifications for tautologies, we will get them all the time.  Our students do not have the same ability to reason logically as we do.*  But rather than merely kvetch about these dang kids who couldn't justify their own existence, the onus is on us to teach the skill of justifying an answer in physics.

*One student's impeccable logic:  "One time I saw some unexplained lights at night.  I called the local airport control tower, who confirmed that they knew of no aircraft operating in my area.  Therefore, I was visited by a space alien."  And no, sorry, I am NOT kidding.

My students seem to respond well to my demand for one of three possible elements to make a justification legit.  They must include either equations, calculations, or facts of physics.  In some problems, only one of these will be of any use; in the question I posed above, any one of them might be useful.  For example, some reasonable justifications:

(1) Using equations:  "Solving the ideal gas law for temperature, T = PV / nR .  Here n is constant because it's a sealed container, and pressure is constant because the problem stated atmospheric pressure the whole way.  The only variable is volume, which is in the numerator.  So, when volume increases, temperature must increase as well."

(2) Using calculations:  "Use the ideal gas law, PV = nRT.  In the initial state, plug in values:

(105 Pa)(0.005 m3) = (1 mol)(8 J/mol K)(T), so T = 62 K initially

Now in the final state:

(105 Pa)(0.010 m3) = (1 mol)(8 J/mol K)(T), so T = 125 K finally

Thus, the temperature has increased.

(3) Using facts of physics:  "An isobaric process looks like a horizontal line on a PV diagram.  Isotherms are hyperbolas assymptotic to the axes on a PV diagram.  So, a horizontal line with increasing volume must jump to an isotherm that is farther from the origin, and thus representing a higher temperature.

Once I've demanded these elements of justification enough times, the class gets the idea.  And when someone is lazy, forgetful, or simply wrong, I don't have to argue about the legitimacy of his answer.  I just ask, "Did you use equations, calculations, or facts?"  If the answer is "no," the student usually hangs his head in shame without any further prompting.