%error = experimental value – theoretical value x 100
theoretical value
The percent error for the first metal, iron or steel, was determined in this way:
%error = 0.099 cal/g °C – 0.107 cal/g °C x 100
0.107 cal/g °C
% error = +- 7.477%
For calculation 2 part 2, I found it for the second metal, lead, in the same way:
%error = experimental value – theoretical value x 100
theoretical value
% error = 0.0361 cal/g °C – 0.031 cal/g °C x 100
0.031 cal/g °C
% error = +- 16.452%
Error Analysis
The error analysis for this laboratory was a percent difference calculation between the accepted value of the specific heat values of iron and lead and their experimental values. The examples of this are in the calculations above. The percent error of the lead was +- 16.452%, which is very high. The percent error for the iron was 7.477%, which is also high. I believe this has to do with the inaccuracy of the calorimeter in insulating the heat from the metals. I also believe that reading the temperature at the high temperature point was difficult because of the construction of the calorimeter. This could have contributed to the random error present. I believe it was random because of my possible inconsistent readings of the thermometer and crude calorimeter.
Discussion:
This laboratory and its exercises are beneficial. The enable a physicist to learn how to find a metal’s specific heat value through experimentation. The use of the calorimeter can help discover this as well as help determine how many cal/g °C are in other objects as well. This could help to determine the identity of an unknown material. I was surprised that the temperature of the water in the calorimeter for the iron test was so much higher than the temperature of the water in the lead test. I honestly thought that the temperatures would be about the same because both metals had been placed in water that was boiling at 103 °C and were of similar masses.
Questions:
- Why was it a good idea to start with room temperature water in the calorimeter?
- It was a good idea to start with room temperature water in the calorimeter so that the heat capacity of the water would not change after the initial recording of temperature.
This would ensure that the change in temperature of the water only occurred due to the
hot metal objects being added.
- Why did we ignore the calorimeter in our calculation, although it is listed in the original equation?
- We ignored the calorimeter in our calculation because the majority of the heat was absorbed by the water and little was absorbed by the calorimeter. It would have been difficult to get a reading of the Styrofoam cups temperature regardless.
- When eating apple pie, you may have noticed that the filling seems to be much hotter than the crust. Why is this? What can you conclude about the specific heat of the fillings vs. the specific heat of the crust?
- The specific heat of the fillings must be much lower so the temperature of the filling rises much higher.
- Is the heat exchange between the metal and the water in the calorimeter by radiation, conduction, or convection? Why?
- The heat transfer between the metal and the water in the calorimeter is through conduction because the heat was flowing directly through the metal into the water.
Conduction is the transfer of thermal energy between two regions of matter due to a temperature gradient. Heat spontaneously flows from regions of higher temperature to regions of lower temperature. This happens until the two regions approach thermal equilibrium(
Results:
In this laboratory I learned how to find the specific heat value for metals using calorimetry. I created a colorimeter by using Styrofoam cups, 1 inside another, and using the bottom of a third cup on top of the others. I then poked a hole to put a thermometer in to measure the temperature of the water. The amount of water for the 2 tests was 25 mL. I made sure to allow the water to sit out for an hour so that it would be at room temperature. When I took the metals out of the boiling water and placed them in the calorimeter, I made sure to do it as quickly as possible to reduce heat loss. I found it difficult to do this without losing heat to through the top hole where the thermometer was and from the calorimeter itself. I then used the data tables above to group my data. After doing that, I used the calculations above to discover the values for the specific heat of each of the metals. The independent variables in the experiments were the metals. The dependent variable was the change in temperature of the water in the calorimeter due to the addition of the hot metals. Depending on the weight and composition of the metals, the temperature change of the water would be different. The results deviated heavily from the expected values. The % error of the specific heat capacity of the first metal was 7.477 %. For the second metal it was 16.452 %. I noticed in the end that my % error for the 2 runs was higher than I expected. This would indicate to me that there was a high degree of error. In my estimates, I would guess that the error had to do with random error in temperature recording and construction of the calorimeter. I also think that the composition and accepted specific heat values of the metals may have been idealized. The metals may not have been 100% lead or iron. The accepted specific heat values may have also been estimated. More testing almost always decreases the likelihood of error, however I do not think it would make a significant difference here. The calorimeter was made of household goods and heat could easily escape. Also the transfer of the metals from the boiling water to the calorimeter takes longer than it should. I think better equipment would help with reducing errors.
Interpretation of Results:
I had known the accepted values of the specific heat capacity of the metals prior to conducting this experiment. I was surprised to find that the temperature of the water in the calorimeter was significantly higher after the iron was added, as compared to when the lead was added. The difference between these two temperature readings was 3 °C. This is a massive difference in temperature for two metals of close masses. The specific heat capacities were similar to the accepted values. These results did support that information, however there were significant % errors. The results made me change my original beliefs and accept the notion of finding specific heat capacity through calorimetry. Before doing this I did not think I could do it. I trust the results, however they could be more accurate with better equipment such as a real calorimeter.
Error Sources and Why:
Errors were caused by many things in this laboratory. First, the equipment was not laboratory grade. The use of Styrofoam cups instead of a traditional calorimeter caused heat to escape. It was also difficult to read the thermometer when it was inside the calorimeter hole. I would have to keep pulling it half way out to get a reading. I know this must have caused the temperature to drop. It also may have caused me not to see the highest temperature reached. It is also possible that the temperature of the calorimeter may have heated up more because I had it too close to the stove on the first run.
