August 28 - Heating Brass Ring, Thermal Expansion Derivations/ Linear Thermal Expansion Demo, Differences in Thermal Expansion, Latent Heat Experiment

Heating Brass Ring

Ring Expansion Prediction/ Result

We took a brass ring and a brass ball and tried to have the ball go through the ring and it wouldn't fit.  We predicted that if we were to heat up the brass ring that the ring would stay the same size and the ball still wouldn't go through.

Ring Expansion 

 The result was that the ring expanded at the same ratio in the same direction (outward) and the ball was able to go through as can be seen in the video.

Thermal Expansion Derivations/ Linear Thermal Expansion Demo

We were told that a metal pole was going to be heated up and that there would be an initial length and a final length and that we were to find an equation for the relationship between the initial length and the final length.  We found an equation but then realized that there was a part missing from this equation, which in this case is the coefficient of thermal expansion (α). We then found the new equation for Thermal expansion for latent heat. 

Equation Derivations

Metal Pole Set-Up

We then took a metal rod that was connected to Logger Pro and heated it with steam and tracked the initial angle and the final angle that the metal rod turned through, the initial and the final temperatures that the rod had throughout the angle turned and found the radius of the rod with a caliper.

Finding Coefficient of Thermal Expansion

Using angular kinematics we solved for the coefficient of thermal expansion for the metal rod by the similarity that ∆L = ∆Ѳ * r .  After plugging in all of the values we found the coefficient of thermal expansion to be 12 x 10^6 1/°C

Differences in Thermal Expansion

Differences in Thermal Expansion (pt 1&2)

We took a metal rod where one side was a metal called Invar and the other side was brass and we were informed that Invar had a very low coefficient of thermal expansion. 

Invar Side Heated

 For the first experiment the Invar side was heated and it was predicted and observed that the metal pole curved towards the Invar because the brass has a higher coefficient of thermal expansion and therefore heats up faster.

Brass Side Heated

 For the second experiment the brass side was heated and the metal pole again curved towards the Invar side because brass has a higher coefficient of thermal expansion. 

Putting Pole in Ice

 For the final experiment the metal pole was stuck into a bucket of ice and it was predicted and seen that the pole curved towards the brass side because it has a higher coefficient of thermal expansion and so therefore it cools down faster.  

Differences in Thermal Expansion (pt 3)

Latent Heat Experiment

Phase Change Prediction and Reality

Phase Change (Teachers Experiment)

We took a glass of ice water that was at 0°C and were told to predict a graph of what would happen when we stuck an immersion heater into the glass of ice water.  Our prediction was what we learned in physics where there is a phase change and then a latent heat of fusion and then another phase change and then another latent heat of vaporization change.  This was wrong, in reality there is an immediate increase in temperature and then once the water really started to heat up the graph actually began to curve up and wasn't even a linear line which can be seen by the picture below which shows an immediate increase in temperature.  The picture also shows that the water didn't boil at 100°C but 97.1°C which was most likely due to natural causes like heat loss from lack of insulation.                                                                                                      

How to have the best results in experiment

After watching the experiment done by the professor we did the experiment ourselves except we preformed the experiment to find out what the values for the latent heat of fusion/ vaporization are and also what the specific heat capacity for water is.  We began the experiment by exploring different ways we could run the experiment with as little error as possible and also found a method for solving for specific heat and for the latent heat of fusion/vaporization.

Phase Change (Our Graph)

Getting water to 0°C 

We started the experiment with 150 grams of ice that was dried off with paper towels to remove as much water as possible and 150 grams of 0°C water. We placed the immersion heater (which had a wattage of 291.2 W) into the glass of water/ice and tracked the temperature change with logger pro and a temperature probe.  After the ice had melted and some of the water turned to steam, we stopped logger pro and weighed the water to find out the amount that had turned to steam, we found that we had lost 38 grams of water to steam.  We then found the time it took for the water to boil and the initial and final temperatures of the water so that we could solve for the specific heat of the water.  

Specific Heat/ Latent Heat of Fusion and Vaporization Values

After solving for specific heat of water we then found the latent heat of fusion and vaporization.  

Values

Our values came very close to the accepted values and our largest percent discrepancy was 33.5%.  After finding the values we then proceeded to propagate uncertainty to find out if our values fell within a range of the true value.

Uncertainty of Specific Heat and Latent Fusion

Uncertainty of Latent Vaporization

For our specific heat, even with our uncertainty of +/-.363035 J/g°C, we did not fall within range of the accepted value.  This is due to factors such as loosing heat by not using a very well insulated cup to preform the experiment and not having an exact time of the two points we marked on our graph. Although our specific heat didn't fall within range, our latent heat of fusion (uncertainty of +/-22.1986 J/g) and vaporization (uncertainty of +/- 313.7415 J/g) fell within range when adding/subtracting our uncertainty value to the experimental value.