25 August 2015: Relationship between Fahrenheit and Celsius, Standard deviation and uncertainty, and Conduction of Heat energy

Purpose:

The purpose of this lab was to find the formula that relates the Celsius and Fahrenheit temperature scales, to be able to find the standard deviation of a set of data points, predict heat transfer by conduction between two substances or objects, and assess the prediction through experimenting. In addition, the rate of heat transfer was studied along with the conditions that affect it in order to derive a formula that represents the rate of heat conduction. Lastly, the specific heat of water was experimentally obtained as well as the uncertainty in that value.

Apparatus:

The above apparatus was used to measure the rate of conduction of heat energy between cold and hot water as well as between hot water and an aluminum can. It was also used with LoggerPro to record the change in temperature of the objects and substances.

The above apparatus was used to experimentally find the specific heat of water by measuring the heat transfer over time by conduction between the 200 mL of water and the heating device. This apparatus was used with LoggerPro to obtain data points and plot a graph.

Experiment:

 The above graph was obtained by plotting the melting point and boiling point of water in degrees of Celsius and Fahrenheit. Using slope-intercept form, the relationship between the Fahrenheit and Celsius scale was derived using this graph.

Next, each group in the class predicted the temperature of the classroom in Kelvins. The average of the predictions were obtained and the standard deviation of the data set was calculation. The temperature of the classroom was predicted to be 294 +/- 2 Kelvin. 

Predictions were calculated that provide the temperature of a system after two substances or objects of differing temperatures came in contact with each other and reached thermal equilibrium through conduction. The left side of the board shows the mixing of hot and cold water of equal masses. The right side of the board displays the mixing of hot and cold water of differing masses.

The mixing of hot and cold water of equal masses was then performed and the temperature after thermal equilibrium was experimentally obtained. As can be seen, the experimental temperature and predicted temperature are similar. The difference is caused by not having exactly equal masses, some heat being lost into the surroundings, and the bodies of water not having the exact temperatures used in the prediction.

The same experiment was done for the prediction of the mixing of hot and cold water of different masses. The experimental temperature was also close to the predicted in this experiment. The difference is seen for the same reasons stated in the previous experiment.

 Conservation of momentum was used to explain why mixing hot and cold water causes the hot water to cool and the cold water to heat up, and why when mixed they reach thermal equilibrium. Heat causes water molecules to move around faster, and when water of differing temperature comes into contact, the water molecules begin colliding with each other. The "hotter" water molecules lose momentum and the "colder" water molecules gain momentum from the resulting collisions, resulting in all the water molecules obtaining the same average speed and therefore obtaining the same temperature.

Hot water and an aluminum can filled with water at room temperature were placed in contact with each other and, through conduction, were allowed to reach thermal equilibrium. As can be seen, the hot water lost more heat energy than did the cold water in the aluminum can. Heat flow through layers was observed and studied.

Six conditions that affect heat transfer and rate of conduction were listed, and were used to explain why the cold water in the aluminum can gained less heat than the hot water lost, shown below.

The formula for conduction of heat energy and heat transfer derived from the list and aluminum can experiment was used to determine to heat flow through a copper and aluminum bar that are in contact with each other and are isolated, not allowing any heat to escape from the system. The copper bar end is at 100 degress Celsius and the aluminum bar end is at 0 degrees Celsius. Using the calculated constant heat flow, the predicted temperature of the faces of the bars where they come into contact was obtained.

 Neither a candle nor a blowtorch (at the lowest setting) heating a balloon filled with water for 10 seconds were able to allow the balloon to pop. This is because water has a high specific heat, causing it to gain much more heat than other substances before it can increase in pressure. In addition, the balloon being made of rubber, which is a poor conductor of heat, is another reason why the balloon was not able to pop in 10 seconds. However, the balloon is thin, making that effect minimal. At the highest setting though, the blowtorch was able to pop the balloon in over 10 seconds from contact. After the balloon popped, water sprayed in the direction opposite of the blowtorch. This is because the blowtorch caused the balloon (with the water inside it) to swing the opposite way by Newton' s third law.

The above graph was obtained when the 200 mL of water was heated through conduction by the metallic heating device. As can be seen, as more heat was added to the water, the temperature of the water was increased. The heat was measured by multiplying the power going through the heating device by the time the heating device was in contact with the water. Using a linear fit, the slope of the graph was found to be:

where Q is heat (J), m is the heat capacity of water (J/degree C), T is temperature, and b is the initial heat of the water. Heat capacity, as defined, depends on the mass of the water and the specific heat of water. This were the formula Q=mcT was derived. Using this formula and the data obtained, the specific heat of water was experimentally obtained.

(To be continued)