Lab Report Day 2 - Thermal Expansion and Latent Heats

1. Heating metal

We have a ring which is initially smaller than a ball. Then we want to heat it up to see whether the ring will expand both outside or outside out and inside in. When we heat the brass plate, the hole gets larger. When we heat it, it expands to all the way. From this, we can tell that the distance between two points increases with the same ratio.

Our Prediction

2. Thermal Expansion

Predict heating a metal, relation between length and temp. 

We write down our prediction formula for it.

L is the length of the metal (while i and f stands for initial and final)

ΔT is the change in temperature.

α is the coefficient of thermal expansion (unit is 1/°C)

From the linear thermal expansion expression, we get the expansion for area and volume as well.

3.Thermal Expansion for Different Metal

We heat two strip that are stick together. We make some prediction on whether it will bend toward to one side. One strip is Invar, and the other one is brass.

By the formula we get from the last picture, we then predict the side the strip will go to the Invar side.  Different metals expand for a different length, so the strip bends to one side. Brass has a higher coefficient of thermal expansion,  so it will expand more. So the Invar side will be shorter.

This is what really happens when we heat the bimetallic strip.

Heat Invar Side:

Heat Brass Side: 

We then dump the two strips into ice, and see which side will it bend to. When we dump it into the ice, they would both be shrunk

Then, we make some prediction that it will bend to the brass side, because brass has a high coefficient of thermal expansion, so the change in length of brass will be big. The brass will be shorter.

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4. Linear Thermal Expansion Demo

A metal rod is heated with stream. Since it has a change in temperature, it will expand. The expansion will make the motion sensor turn, so we can measure the angle it turns. For a period of time, we can find the coefficient of thermal expansion.

By using the formula for linear thermal expansion, we can use the information we know to find α, the linear coefficient of thermal expansion. From the calculation, we find out that α is 12.2*10^-6 (1/°C),  which is the coefficient of steel. 

Temperature vs Time Graph

5. Latent Heat

In this experiment, we are going to use a cup of iced water and an immersion heater. We use an immersion heater to heat up the water and measure the time when the phase changes (from solid to liquid, liquid to gas). We predict the Temperature vs. Time graph.

Temperature vs. Time graph.

Here's the procedure to calculate the heat capacity for water. Latent Heat of Vaporization for water and Latent Heat of Fusion for water. 

 Experiment Set Up

We do this in order to get a 0 degrees water.

Temperature(℃) VS Time(s) graph experimentally.

 As we can see, the temperature required to boil water is about 97 °C, which theoretically should be 100°C. This can be caused by the pressure different from standard pressure, and the systematic error of LoggerPro and the probe. 

Calculation for C(H2O), Lf and Lv

Propagation for Uncertainty 

(We propagate the uncertainty. For the measured value, we take 1/2 of the smallest increment)

Results:

From our results, I can see that the experimental value for Lf and Lv are smaller than the theoretical value, while the experimental value for c is bigger than the theoretical value. Our value are not covered by the uncertainty. It could be caused by many reason. The heat flows outside the cup since the cup is not insulate. The reading can also cause the error. The reading are not very accurate. The LoggerPro itself has some systematic errors too. Those factors causes the experimental value differ from the theoretical value. None of the values are covered in the uncertainty, however, our experimental value has a low percent discrepancy from the true value, which is good. We get 2.71% off for the Lf, 3.97% off for the c,  and 2.71 percent off for the Lv.

Summary

In today's lab, we learn that while heating things, every thing will expend out, which means it expands all the ways. Any two points will have distance increase by the same ratio. While heating a metal, it expands by a ratio which is coefficient of thermal expansion. The different expansion rate can cause two metal to bend. The Temperature vs. Time graph is not like what we previous learn from chemistry. While heating iced water, the temperature will increase instead of stay 0°C. We learn how to calculate the coefficient of thermal expansion, how to calculate the latent heat of fusion, vaporization and the specific heat.