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Saturday, June 9, 2012

Methodology and Results: Action-reaction and heat engine models

Installing MathJax in Blogger for LaTeX Equations Linda Yezak of Author Culture applied to writing Newton's Third Law of Motion: for every action, there is an equal and opposite reaction. Mathematically, we say that if mass $A$ exerts a force $\mathbf F_{AB}$ on mass $B$, then mass $B$ exerts a force $\mathbf F_{BA}$ on mass $A$, such that \begin{equation} \mathbf F_{AB} = -\mathbf F_{BA}. \end{equation} Since this is a vector equation, then the magnitudes of these two vectors are equal, $F_{AB}=F_{BA}$, and their directions are opposite, as expressed by the minus sign. What Yezak is saying that if character $A$ acts on character $B$, character $B$ must show his reaction. If we name $A$ as Anna and $B$ as Bob, then it is not enough to say that Anna spanked Bob. Bob must show a reaction. He may ask, "Why do you strike me?", in the same way as Christ asked the soldier of Annas the High Priest (c.f. Jn 18:23).

In physics writing, $A$ can be thought of as the Methodology and $B$ as the Results. If in the Methodology you say, "we measured the temperature of the water as a function of time," then in the Results you must provide a table showing the relationship between temperature $T$ and time $t$ or you must provide a figure showing temperature in the vertical axis and time in the horizontal axis. Whether you use a table or a figure, you must show units of measurement. The temperature may be in Celsius or Kelvin. The time may be in seconds, minutes, or hours. A number without units is not a physical quantity. 

One example of a graph of the rise of temperature vs time of water is shown in Chem Team. You will see that there are 5 major features: 
  • Ice rises in temperature until the freezing point of $0^\circ$ C.  The graph is linear with positive slope
  • Ice melts at $0^\circ$ C.  The graph is horizontal until the amount of heat absorbed is equal to the heat of fusion
  • Liquid water rises in temperature to $100^\circ$ C.  The graph is linear with positive slope
  • Liquid water changes to steam at $100^\circ$ C.  The graph is linear until the heat absorbed is equal to the heat of vaporization
  • Steam rises in temperature.  The graph is linear with positive slope.
In story writing, when Anna hits Bob and Bob asks, "Why do you hit me?", The story does not end there.  Like a boulder rolling from the hilltop, the story should move forward and gain momentum like a heat engine: Anna, Bob, Anna, Bob, Anna, Bob,.....  We can see this, for example, in Shakespeare's Julius Caesar, Act 3, Scene 1:

  • Brutus kills Caesar.
  • Caesar says, "Et tu, Brute?  Then fall Caesar!"
  • Caesar dies.  Brutus and company bathe their swords in Caesar's blood.
  • Brutus speaks about Caesar.
Notice the engine cycle: Brutus, Caesar, Brutus, Caesar, Brutus, Caesar,....

Similarly in writing the Results, there should always be a discussion that relates it to the Methodology.  That is why the section is rarely called Results but Results and Discussion.  You get this graph, because you used this water.  You varied the heat input by increasing the fire, and the result is a shorter time interval at the phase changes.  You lessened the mass of ice, but also lowered the heat input; the the time interval for the phase changes remain the same.  Method, result, method, result, method, result,....  This is the heat engine that drives your Results and Discussion.

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