25-Aug-2015: Calculating the specific heat of water through experimentation

     The purpose of this experiment was to find the specific heat of water. The apparatus' used were an immersion heater, watt meter, and a thermometer hooked up to logger pro. 

The thermometer and immersion heater submerged in the water.

The immersion heater plugged into the watt meter, which gave a readout of the power output of the heater.

     The experiment asked for the immersion heater to be placed in 200 mL of water for 20 seconds. While it was submerged, the water was to be stirred with the thermometer while logger pro collects the temperature for the 20 seconds. The experiment gave a graph of temperature vs time.
     To find the specific heat of water, the following equation was used:

Heat Capacity=mass*specific heat 

or 

C=m*c

Since the volume of water was assumed to be exactly 200 mL, and the density of water is 1 g/mL, the mass of the water was found to be 200 grams. That leaves the heat capacity as the other variable needed to solve the equation for the specific heat. 

     The watt meter showed an output of 284.8 w by the immersion heater. By multiplying the power by the time the heater was submerged, the energy was found. Below is the calculations and data from logger pro.

     If a graph of heat vs temperature is created, then the slope would be the heat capacity of water. To do that, a new calculated column was created in logger pro. In that column, the energy found in the above calculations was multiplied by each point in time during the experiment. This gave values for heat at every point. The graph of heat vs temperature was plotted and is shown below.

A linear fit was done on only the part of the graph that was close to being straight. This provided a slope, which is the heat capacity.

This particular experiment resulted in a heat capacity of 1134 J/(degree C). Now the specific heat was solved for with the equation from earlier. This resulted in a value of:

c=5.67 J/(g*degree C)

     The experiment had uncertainties, however, and a number must be reported along with the specific heat. There were uncertainties in the mass of water. A beaker was used to contain the water, and beakers are not known for precision measuring. There was uncertainty in the watt meter and in the logger pro thermometer. If the water was not stirred properly than the distribution of heat in the water was also uncertain. Overall, based on the way this experiment went, a safe assumption for an uncertainty percentage would be in the 15% range. As a result, the specific heat is multiplied by 15% to give an uncertainty range, and the final answer for the specific heat of water based on this experiment is:

c=5.67 J/(g*degree C) +- 0.85

This number does not fall within the accepted value of 4.186. Therefore the experiment was not accurate and should be repeated for better data.