Thermal Expansions and Latent Heats

Our hypothesis which states that the brass plate will expand.

Thermal Expansion of a Invar/Brass plate.

Thermal Expansion of an Invar/Brass Plate.

A rod with a unknown coefficient of linear expansion is getting hot steam blown onto it, which then turns a pulley of known radius. This equation uses the linear thermal expansion formula however since we only have the amount of radians the pulley turned and the initial length of the rod it is slightly modified.  From our solution it would be highly probable that the rod is made of steel.

A mixture of water and ice both at 0°c are heated at a constant rate. This graph shows how the latent heat of fusion ice is not so clearly defined, which means the ice doesn't all melt then start heating up but in fact the water heats up while the ice is melting.

Practice problem where we solve for the amount of water needed so that the final temperature is 22°c

Procedure to the Ice Water Lab

Known/Derived Quantities
Q=mLf, Lf=44,000/99.8=440J/g

Temperature vs Time Graph
In our timing we found that the ice melted in 2 mins and 28 seconds, and from there we found the latent heat of fusion of water to be 440 J/g.
Next we found let the water boil for 25 seconds. In that time we found that 3.35 g evaporated and that 7440 J were transferred into the water and that the latent heat of vaporization was 2210 J/g.

Heat/Mass vs Temperature
This graphs slope tells us the specific heat of water for our experiment, which is 4.194 [J/g-K] compared to the accepted 4.179 [J/g-K]

We used the formula for latent heat of fusion and latent heat of vaporization, then did some fancy propagation of uncertainty. However to do this we needed the uncertainty of all the components in the formula luckily i knew this from countless 4B labs and even wrote down what uncertainties we needed on the 5 steps to do this lab.
(uncertainty for power was 2J to acount for the fluctuation of the machine and so to accommodate we increased it.)
(Uncertainty of mass was made larger because of how the graduated cylinder is marked and because the ice was melting while we weighed it.

For this uncertainty my group and I did something clever, since we did not use the equation to find specific heat we decided it would be best to approach this by somehow incorporating our graph. What we did was jot down 8 coordinates on opposite sides of the graph from there we found the slope of the two points using y-y1/x-x1=m then we used the a standard deviation to find the uncertainty in the slope, which we defined to be the specific heat of water .

A systematic error occurs in the latent of fusion, because our equation only takes into account the ice turning into water and not the energy going into that water heating up.