We wanted to record the logistic growth of temperature while making caramel on the stove. We used a candy thermometer to record the temperature of the mixture every thirty seconds and a thermal gun to determine the temperature of the stove. In addition, we noted every time there was a change in stove temperature or another ingredient was added. This is significant because it marks the beginning of a new equation. A change in stove temperature changes the outside source of heat, which affects the calculations needed to determine the equations. The addition of a new ingredient changes the specific heat of the total mixture, which will affect how quickly the caramel changes temperature. We conducted two trials, adjusting for errors in the second trial.

**First Trial:**

We refer to this as the first trial only because we did it before the second. In reality however, this was the “Experimental Trial” where we tried different techniques for measuring temperature. In this one we use a thermal heat gun and a candy thermometer. We found that the candy thermometer was more accurate for making caramel. The data in this trial is accurate but there is some margin of error because of inconsistent stirring and measuring of temperature.

—DataTable*–

At first, we used Newton’s Law of Cooling () to calculate by hand four separate equations for the heating of caramels. We used two data points, the initial and the final temperature within the range of time, to determine the equations. Because of this, the equations became heavily estimated; a line of best fit rather than an equation that accurately reflects the data.

As you can see by this graph, the equations that we calculated were not very accurate.

We then decided to use Desmos to give a more accurate equation. By plugging in variables that adjust with each additional data point the four equations found fit almost every data point.

In order to make soft caramels it is necessary to heat the caramel up to 248°Fahrenheit. However, we had a temperature error with the candy thermometer and the mixture was heated to 270°F not 248°F. This caused the caramel to be a hard candy rather than a soft chewy caramel. Still yummy, but slightly harder to eat.

*Temperature is in Fahrenheit and Time is in Minutes

**Second Trial:**

In the second trial, we adjusted for our temperature error by not heating the mixture as quickly. This ensured that it would only heat to 248°F. In the first trial we focused on getting real data rather than making caramels. In this trial however, we focused on making the caramels correctly. We had more experience at this point and could coordinate our efforts to record temperatures more accurately and stir the mixture constantly.

In the second trial, we again attempted to determine our own equations using the initial and final temperature of each section.

Again the equations did not fit the data points very well. With that being said, they did fit much better than trial one. This is because we did a better job keeping the stirring of the mixture constant, along with a more accurate reading of the data.

Using Desmos, we repeated the same process as trial one and determined a continuous equation for the equation.

From this experiment we discovered that slowing heat caramels is the key to success. Especially when it comes to bringing the mixture to to final 248°F at the end. Unlike water (which has a constant specific heat) caramel’s specific heat will change as more water boils off, leaving a more concentrated mixture behind. Because of this, it is necessary to keep the mixture boiling but with the minimum amount of heat necessary. The”blue section” of each graph (the second curve) marks the boiling of the cream, corn syrup, sugar, and salt mixture. If this mixture was water the temperature would remain a constant 212°F; the slope would be zero. However, because there is a continuous change in specific heat the slope is not constant but rather a curve.

**Recipe For Vanilla Caramels: **

Ingredients:

- 2 cups sugar
- 2 cups warm cream
- 1 cup corn syrup
- ½ t. salt
- ⅓ cup butter
- 1 t. vanilla
- ½ cup nuts

Directions:

In a large saucepan mix sugar, 1 cup of cream, corn syrup, and salt. Cook, stirring for 10 minutes, (at boiling). Add remaining cream very slowly so that the mixture doesn’t stop boiling. Cook 5 minutes longer. Stir in butter, 1 t. at a time. Cook slowly to “firm ball” (248°F). Remove from heat, add vanilla and nuts, mix gently.

Pour into a buttered 8x8x2” pan and cool. Turn onto a board, cut into squares.

Thanks for reading!!

🙂 Rebecca Castonguay & Emily Carberry