Temperature Scales; Heat Transfer and Energy Exchange (First Day)

Spring 2015
24th of February's Class

Temperature Scales
We have a refresher lesson on temperature scales (Celsius, Kelvin, Fahrenheit).

We were taught how to find the formula that relates Celsius and Fahrenheit, through empirical methods. First, we create a graph of Fahrenheit vs Celsius. Fahrenheit will be in the y-axis while Celsius will be in the x-axis.

It is shown in the top left corner of the image posted below.

Calculation Steps:
-The freezing point of water in Fahrenheit is 32 degrees, while it is 0 degrees in Celsius.

-The boiling point of water in Fahrenheit is 212 degrees, while it is 100 degrees in Celsius.

-Since Fahrenheit is the y-axis, when we create a right-angle triangle with the graph, the height of the triangle would be 212 - 32 = 180 units.

-Since Celsius is the x-axis, when we create a right-angle with the graph, the length of the triangle would be 100 - 0 = 100 units.

-The slope of the graph would then be equals to Height / Length = 180 / 100, which is reducible to 9/5

-We can observe that the graph does not start at 0 for the y-axis, therefore we have to add 32 units as a constant to the Celsius to compensate for the difference.

-This leads us to the line equation of y = (9/5) x + 32

-This is the conversion formula for Celsius to Fahrenheit, we just have to replace the x value with the desired degree Celsius.



Uncertainty
We also did an exercise for calculating uncertainty when there is one experiment, that is done multiple of times. We were made to guess the room temperature that we were in. The image below shows how we did it.

Calculation Steps:
-Add all the estimated guesses together and find the average, which would amount to 295.33 degree Kelvin.

-Find the differences between the average and each estimated guess, and square each of the differences.

-Add all the squared differences together and divide them by the number of guesses made, to get 2.9016.

-Square the number obtained from the previous step, to get 1.703.

-The plus and minus of 1.703 degrees Kelvin added to the average 295.33 degrees Kelvin is the uncertainty.



Heat Transfer
Professor did an experiment where he had an aluminium can filled with hot water and he placed it into a cup containing cold water. We were tasked to calculate the specific heat of Aluminium.

The variables are as follows:
Mass of Hot Water: 137g
Mass of Aluminium Can: 50g
Mass of Cold Water: 150g
Temperature of Cold Water: 22 Degree Celsius
Temperature of Hot Water: 65.6 Degree Celsius
Final Temperature: 34.4




Temperature Equilibrium
We also did an exercise to find the equilibrium temperature in the middle of a material with different temperatures and material on its two ends.

The first image uses the formula of

To get the Q, which is the heat flow through the copper part of the metal bar. A is the cross sectional area, Th is the hotter temperature, Tc is the colder temperature and Rt is the total insulation given by the copper and the Aluminium.

The second image uses the formula of

K is the conductivity of copper, A is the cross sectional area of metal bar, delta T is the change in temperature (Final Temperature minus Initial Temperature), and L is the length of the metal bar.