Friday, February 27, 2015

Temperature Conversion, Uncertainty, Heat Transfer, Thermal Conductivity, and Power

Spring 2015, Prof. Mason

24 February 2015

Understanding Temperature Conversions:

We started the day with converting between temperatures that we have previously learned a while ago (Celcius, Kelvin, Fahrenheit).
Given a chart of difference in Celcius and Fahrenheit, we made a graph of the relationship between these two temperature scales. From this graph, we recalled the formula to convert Fahrenheit to Celcius [K= *C(9/5)+32]. On the right side of the graph, we were finding the Kelvin of the Fahrenheit given, which was 74*F. We converted it into *Celcius before converting it to Kelvin because we found this way to be easier to approach. From this calculation, we found the answer to be 295 K. 

Understanding Uncertainty:

When professor collected the data from each group, the answers were ranging between 293 K-298 K. Thus, we needed to find the uncertainty of our answers to see whether or not our answers are valid. To find the uncertainty, we used standard deviation, which we know the formula to be sqrt(sum of((X-avg)squared)/n or n-1). Using this formula, we found the answer to be 295 +/- 1.740 K, but since many of our answers were in three significant figures, by default, we rounded the average and uncertainty to be a whole number instead of decimals. Therefore, our final answer is 295 +/- 2 K.


Understanding Heat Transfer:

We learned in the past from either phys 4A or chem about heat transfer. We refreshed our memory that the formula of heat transfer as we know to be Q = mc(delta T). We conducted two experiments regarding this topic:

1) We filled up two cups with water at a different temperature, cold and warm. Mass and temperature of each cup were measured, and specific heat of water is to be 4.18 J/g*C. We calculated what the final temperature would be if we mix the water from these two cups using the formula of heat transfer. We found the answer to be 47.7*C.











2) 
We filled up one cup with water in warm temperature and an aluminum can with water in colder temperature. Mass and temperature of cup and can were measured, and specific heat of water is again to be 4.18 J/g*C. We placed the can in the hot water that was in the cup. In this calculation, the transfer of heat in different medium have different specific heat. In this case, the can must be 
calculated separately from the cold water, and in this experiment, we needed to find the specific heat of the can. We found the answer to be 19.41 J/g*C. We believe this answer to be invalid because we did not consider the temperature of the surroundings. Since the can is not completely submerged, the top of the aluminum can has contact with the free surface. Therefore, we have to take into consideration heat loss/gain to the surroundings. The ratio of the can's surface area that submerged against the non-submerged greatly affected this calculation.

Understanding Thermal Conductivity:


We were given two different materials of metal that attached together with nothing in between, copper and aluminum. The end side of the copper metal was 100*C and aluminum was 0*C. We were then asked to find the final temperature of them, given the heat transfer of them, the surface area, and the R-value of each metal. The answers should be the same does not matter where we approach it from, copper side or aluminum side because both surface are touching with no disturbance in between. We found the final temperature to be 67.9 *C.



Understanding Power:

For our last experiment of the day, we heated a room temperature water with an immersion heater. The heater we know to have a power of 300 W. We needed to find how much heat it generates if we were to leave the heater for about 20s. Using the formula that we have already learned before, P = Q/t. We found the heat generated to be around 6000 J.