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ELECTRICAL HEATING INVESTIGATION

I have divided my advice for the write-up into the official four sections.  You do not need to arrange your account exactly into these four sections; all that matters is that these things are all covered somewhere.

The Planning section is fairly easy:

• Make sure you have explained how you made sure it was a fair test.  Which factors did you vary?  Which did you keep constant?  {Be clear that this is not to do with experimental accuracy, repeating, and so on...}
• You need a clear prediction, preferably not just a vague "if this increases, then that will increase" sort of prediction.  Suggesting that something is proportional to something else, and therefore will give a rising straight line through the origin, is a good move.
• Explain what you think is happening, using your wide knowledge of physics ...  Talk about conduction, convection, and radiation.  Draw diagrams to show heating.  Talk about heat loss, and where it is likely to be occurring.  Talk about energy conversion.
• Harder: Bring in the mathematical equations of electricity.  P = VI, and V = IR (Ohm's law).  P is the electrical power used up (the electrical energy used up per second), which for us is also the heat produced per second.  If the voltage V doubles, presumably P doubles.  Well, only if I remains constant.  But I increases when V increases, according to Ohm's law, and common sense.  So if, say, you double V for the heater, then you will double I through the heater as well.  But the power is these two multiplied together, so if both of them double, P will double-double; it will increase x 4.
• This means that the heating effect of electricity is proportional to the voltage squared (V²).  Indeed, P = V²/R is an alternative formula for electrical power.  And this means that a graph of the rate of rise in temperature plotted against voltage would not be a rising straight line, but instead a rising curve.  y = x² is the equation of a parabola, a standard mathematical shape.

The Observing section is almost certainly fine - you should have plenty of data. 

• If you have done some repeats, at the same voltage, only plot the average resulting temperature rise.
• The tables of results must have proper boxes, and headings with the quantity, the symbol, and the unit. 
• Show one complete calculation.  Show, for example, how you calculated a, the overall rise in temperature per minute.

The Analysing section is a bit more tricky.

• Graphs must have labels and units on the axes.
• Never join the data points.  Always put on a smooth average trend-line.
• Perhaps you can put on two trend-lines - either of which could be the true trend.  Now you can discuss which of the two trends seems more likely to be true.
• A straight-line trend - actually any trend - that doesn't go through the origin cannot physically be right.  If the line cuts the x-axis, it means that some amount of voltage won't produce any rise in temperature at all.  How could this be?  After all, if there is a V, there is an I, and therefore a P, and therefore heat is being generated, and therefore the temperature must rise.
• Does your data fit - to some extent - with a rising curve?  If it does, then you can link this result to the theory in the planning section (above), where doubling V quadruples a, and tripling V increases a x 9.  Is this roughly true for your curve?  You can take a nice round number for a first value of V, read off from your best-fit curve a corresponding value of a, then double V and see what happens to a on your graph - does it roughly quadruple?

The Evaluating section is the hardest.

• Was your data all exactly on your smooth average trend-line (or lines)?  I very much doubt it.  Why not?  You need to explain this, referring to experimental inaccuracies in your experiment.
• If the temperature increases were small, just a few degrees, then the inaccuracy in your thermometer readings is very significant.
• If the temperature rose much above room temperature, then the water will have begun to lose quite a lot of heat to its surroundings. - and lost more, the hotter it was, which is the say, the higher the voltage that was being applied.
• Write quite a long section describing a further experiment that you could have done.  One possibility is to investigate the rate of rise in temperature of different masses of water, keeping the voltage the same.  Another is to investigate the rate of rise in temperature if the beaker was thoroughly insulated.