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Measure the specific heat of water and other fluids

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Step 5: Conclusion

In this experiment, the specific heat of water was measured by heating a small quantity of water with a known power input, and measuring the temperature change over a period of time. Experimental error due to heat transfer to or from the surroundings was minimized by taking measurements an equal amount of time before and after the ambient temperature was reached.

The heat capacity of water was determined to be: 4.4 +/- 0.2 J/g/degree C.
This agrees with the known value of 4.2 J/g/degreeC

The same experiment could be used to measure the heat capacity of any substance that is a liquid at room temperature. For liquids that are electrically conductive, the resistor and wires should be insulated so that they do not come into direct contact with the liquid. Pure water is actually a poor conductor of electricity. It only conducts well when impurities (such as salt) are present. Some other household substances you might consider testing are: vegetable oil, olive oil, motor oil, rubbing alcohol.

Sources of error
Sources of error in this experiment include measurement error, heat transfer to the surrounding air, and cooling due to evaporation. Measurement error is likely to be the most significant of the three. With basic equipment, the specific heat can only be measured to an accuracy of about +/-5%.

Improvements
Accuracy could be improved by several methods:
1. Reduce error due to heat transfer and evaporation by using an insulated container such as a styrofoam cup with lid. I used what I had.
2. Reduce measurement error with better instrumentation. The voltage and current could be measured more accurately with a digital multimeter rather than relying on the power supply display. A higher resolution thermometer could also be used.
3. Reduce measurement error by increasing the voltage. Increasing the value of V will results in increased values of I and (T2-T1) as well. Since the absolute error in each of these quantities is fixed, increasing the values will decrease the percentage error. However, there is a trade-off since at higher or lower temperatures, the error due to heat transfer with the surroundings will increase.
4. Reduce measurement error and heat transfer error by curve fitting. Rather than simply using a datapoint 10 minutes before ambient temperature and another datapoint 10 minutes after, it would be more accurate to fit a polynomial curve to all the data points and calculate the rate of temperature change (the slope of the curve) at the instant the fluid reaches the ambient temperature. At this instant, there should be no heat transfer to or from the surroundings, so the rate of temperature change would be solely due to the input of electrical power.

Further Reading
For a detailed description of specific heat including known values for a variety of materials see Wikipedia's entry on Specific Heat Capacity.

For details of other interesting experiments and projects see my website IWillTry.org.
 
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