At the beginning of class we had a group quiz and were asked to create a circuit in which the two bulbs were as dim as possible using 5 wires, 2 light bulbs, and 2 1.5V Batteries. In order to get the bulbs as dim as possible with the given equipment we decided to line the bulbs up in series and the batteries in parallel. The bulbs were so dim only a small hint of orange could be seen in the filament inside the bulb.
In class there was an experiment set-up in which 200 grams of water was placed in a cup along with a coiled wired heater. The length of coiled wire in the heater was 42 cm. It was attached to a 4.5 V battery and placed in the cup of water for a total of 10 mins. A temperature probe placed inside of the cup recorded the temperature as it changed in logger pro. During the 10 mins the "heater" was submerged in water we calculated what the temperature change of the water should be given the length of the wire, voltage of battery, mass of water, and any necessary constants. Our calculations are shown below.
After we calculated the resistivity (R) of the wire (6.5 Ω) we determined the current (I) for two cases. The reason this was done was because depending on which resistivity constant was used the result for R may have been slightly different. Using this difference we found an uncertainty in current. We then proceeded to calculate the power and found its uncertainty according to the difference between the two cases. At this point we had all the necessary values to calculate ∆T. Using Q=mc∆T and Q=P⋅t we found that the theoretical temperature change of the water should be 2.22°C.
In order to find the uncertainty we propagated the equation for ∆T according to the uncertainties we knew. Giving us a final answer of ∆T=2.22±0.57°C.
The same exact experiment was run again, however this time our voltage was doubled to 9.0V and we were asked to follow the procedure to calculate ∆T. After all the calculations were finished it was found that ∆T=8.90±2.38°C.
The above picture shows the temperature change results from logger pro for each experiment. The blue data set was the 9.0 V experiment and the red data set was the initial 4.5 V experiment. According to logger pro for the initial experiment the temperature started at about 23°C and concluded at about 25°C for a 2°C temperature change. The doubled voltage experiment started at 24.6°C and ended at 32.1°C for a 7.5°C temperature change.
Contrary to what most may have expected the change in temperature of the system did not double, it actually almost quadrupled. The reason for this can be shown mathematically.
When we look at what occurs to the current, power, and temperature change we see why ∆T did not double as the voltage was doubled. For both experiments R was the same, however for current the voltage doubled resulting in a value for current that also increased by a factor of 2 because current and voltage are proportional. When the new current is substituted into the power equation we see that the voltage here is actually 4 times that of the initial power calculation. The reason for this is that the current was doubled and the voltage was doubled. When these two values where multiplied to find power the power quadrupled. This value then carried into the ∆T equation thus quadrupling the temperature change.
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