Research Question: What is the effect of the specific heat of various substances on the temperature of hot coffee?

Table of Contents:

In this investigation, I plan to determine and record how the specific heat of various substances affects the temperature of hot coffee. I thought of this due to a common problem I run into on a daily basis; since I have to go to school almost every day, I rarely have time to wait for my coffee to cool down. Due to this, I was struck with a question when my class began studying thermodynamics; how can I use specific heat to solve my daily issue? When two fluids of different temperatures are mixed, the resulting fluid must eventually balance out. This is why, for example, pouring cold coffee into a hot cup of coffee will slightly cool the coffee; the mixture is reaching an equilibrium between the two temperatures. The resulting temperature of the coffee/milk mixture is lower than that of the coffee alone, but higher than that of the milk alone. There are many variables that go into what exactly this final temperature will be, such as the temperatures of the respective substances, the mass of the substances, and the specific heat of the substances. Since different fluids have different specific heat, this has led me to the final question I aim to answer: what is the relationship between the time it takes to reach a temperature equilibrium and the specific heat of fluids?

I plan to use ten different fluids, those being milk, apple juice, pulpless orange juice, water, soda, lemonade, cranberry juice, coconut water, fruit punch, energy drink. My independent variables will be the time it takes for the mixture to cool, while my dependent variable will be the specific heat of the substances. My control variables will be the starting temperatures of everything and the mass. I believe that, because of how easy it is to heat and cool water, this will be the one that cools the coffee the fastest.

Hypothesis: The higher the specific heat of the substance, the cooler it will make my coffee when they are mixed.

Scientific Reasoning: The specific heat is the amount of heat required to raise the temperature by one degree Celsius. Therefore, a lower specific heat would heat faster. Inversely, something with a higher specific heat would heat up faster. By finding the specific heat of things usually added to coffee, I can determine which is more effective by comparing their specific heats and finding the one with the highest specific heat.

Variables:

Independent Variable:

● Substance being used

Dependent Variable:

● Specific heat (found using the formula mcΔt=mcΔt)

Controlled Variables:

● Amount of boiling water (250 mL)

○ Reason for controlling variable: consistency, an attempt to ensure there aren’t too many errors in the data

○ How it will be controlled: the boiling water will be measured before being mixed.

● Temperature of water (83 degrees Celsius)

○ Reason for controlling variable: consistency

○ How it will be controlled: I will attempt to pour the water directly into the measuring cup after being boiled so little heat is lost.

● Amount of substance being tested (50 mL)

○ Reason for controlling variable: consistency

○ How it will be controlled: the substance will be measured out to 50 mL before being mixed.

Equipment:

● A calorimeter built from the following materials:

○ One paper cup

○ One thermos with a lid and a small hole in that lid

○ A thermometer

● 6750 mL total of boiling water

● 150 mL of coffee

● 150 mL of milk

● 150 mL of sugar

● 150 mL of agave blue syrup

● 150 mL of coconut oil

● 150 mL of beer

● 150 mL of wine

● 150 mL of Pepsi

● 150 mL of A1 steak sauce

● Electric kettle

● Measuring cups

Fig 1. The set up (not pictured: the electric kettle that the water is boiled in, timer)

Methodology:

Set water to boil (this will take a few minutes)
Measure out 150 mL of substance being tested
Measure temperature of substance
Write down temperature
Pour out water once it has boiled into 250 mL measuring cup
Pour water into thermos and screw on lid (so less heat escapes)
Measure temperature of water
Write down temperature
Pour in substance
Measure temperature immediately after mixing
Write down temperature
Repeat above process three times per substance
Calculate the specific heat for each trial using mcΔt=mcΔt with the first mcΔt being water (250*4.186*(Initial temp - final temp)) and the latter mcΔt being the substance (150*c*(Final temp - Initial temp)) and solving for c

○ Example: (250*4.186*(80-60))=(150*c*(60-40))

■ c=6.97666667 KJ/kg

Find the average specific heat for each substance
Compare the average specific heats
Conclude and evaluate

Trials:

Trials for Milk

	Initial Temperature of Milk	Initial Temperature of water	Final Temperature	Specific Heat
Trial 1	9	77	69	2.790666667
Trial 2	10	83	70	4.050967742
Trial 3	10	84	69	5.321186441

Average Specific Heat: 4.054273617 KJ/kg

Trials for Coffee

	Initial temperature of coffee	Initial temperature of water	Final temperature	Specific heat
Trial 1	46	83	77	4.186
Trial 2	48	83	78	3.805454545
Trial 3	49	85	79	4.330344828

Average Specific Heat: 4.107266458 KJ/kg

Trials for Sugar

	Initial temperature of sugar	Initial temperature of water	Final temperature	Specific heat
Trial 1	23	85	75	3.949056604
Trial 2	22	86	75	4.263518519
Trial 3	23	85	76	3.6225

Average Specific Heat: 3.945025041 KJ/kg

Trials for Coconut Oil

	Initial temperature of coconut oil	Initial temperature of water	Final temperature	Specific heat
Trial 1	22	85	76	3.488333333
Trial 2	22	87	77	3.805454545
Trial 3	22	86	77	3.424909091

Average Specific Heat: 3.57289899 KJ/kg

Trials for Agave Blue Syrup

	Initial temperature of agave	Initial temperature of water	Final temperature	Specific heat of agave blue syrup
Trial 1	21	86	74	4.651111111
Trial 2	21	87	75	4.566545455
Trial 3	21	87	75	4.566545455

Average: 4.594734007 KJ/kg

Trials for Beer

	Initial temperature of beer	Initial temperature of water	Final temperature	Specific heat of beer
Trial 1	22	81	75	2.462352941
Trial 2	22	85	76	3.6225
Trial 3	22	82	75	2.872745098

Average Specific Heat: 2.985866013 KJ/kg

Trials for Wine

	Initial temperature of wine	Initial temperature of water	Final temperature of mixture	Specific heat of wine
Trial 1	19.5	85	73	4.784
Trial 2	20	86	76	3.805454545
Trial 3	19.5	86	76	3.704424779

Average Specific Heat: 4.097959775 KJ/kg

Trials for Sunflower Oil

	Initial temperature of sunflower oil	Initial temperature of water	Final temperature of mixture	Specific heat of sunflower oil
Trial 1	20	83	78	1.835964912
Trial 2	18	85	82	1.00464
Trial 3	20	85	82	1.0465

Average Specific Heat: 1.295701637 KJ/kg

Trials for A1 Steak Sauce

	Initial temperature of A1 steak sauce	Initial temperature of water	Final temperature of mixture	Specific heat of A1 steak sauce
Trial 1	10	85	71	4.764552846
Trial 2	10	86	72	4.651111111
Trial 3	10	89	75	4.5784375

Average Specific Heat: 4.664700486 KJ/kg

Trials for Pepsi

	Initial temperature of Pepsi	Initial temperature of Pepsi	Final temperature of mixture	Specific heat of Pepsi
Trial 1	22.5	87	76	4.470485437
Trial 2	22.5	88.5	77	4.498971963
Trial 3	22.5	89	78	4.22440367

Average Specific Heat: 4.397831367 KJ/kg

fig 2. Chart comparing the specific heats of the substances tested

Data File: Text | Excel

Conclusion:

As evidenced by the chart above, it seems as though A1 steak sauce would be the most effective at cooling anything with a lower specific heat than it, which coffee has. However, due to the fact that this is testing cooling coffee to drink, it would be the most advantageous and make the most sense to use the agave blue syrup in order to cool coffee. The least effective thing to use to cool my coffee would be the sunflower oil. My hypothesis was proven correct the higher the specific heat, the cooler the mixture would be, as evidenced by the final temperatures I calculated. Therefore, the higher the specific heat of the substance, the more effective it will be as quickly cooling coffee.

Evaluation:

Although I did do my best to even everything out, there are many inconsistencies that may have skewed the results. These errors are primarily human error, the boiling water being varying temperatures, not all substances being the same temperature, and the slowness of the temperature to drop when the ingredients were mixed. If I were to repeat this experiment, I’d try to get all the ingredients to the same temperature first prior to mixing them so there would be a consistent temperature. I’d also get a better thermos, since I suspect heat may have escaped through the hole in the top of the thermos.

Related Websites:

http://www.chegg.com/homework-help/questions-and-answers/1-densities-specific-heat-coffee-milk-different-water-denisty-coffee-density-milk-density--q3893933

This is a link to a simple calorimetry problem that is about coffee, like the problem I was solving for my experiment.

http://chemcollective.org/activities/autograded/115

Both of the above sites are about the specific heat of coffee. The one directly above is another problem about the specific heat of coffee, which is again what I myself was solving.

https://www.engineeringtoolbox.com/specific-heat-capacity-d_391.html

The above is a list of the specific heats of many different materials, which is something I made myself by finding the specific heats of many different materials.

http://theengineeringmindset.com/specific-heat-capacity-of-materials/

The above is another list of the specific heats of many different materials, which again is what I myself was making when finding and writing down the specific heats of the materials I was using.

http://www2.ucdsb.on.ca/tiss/stretton/database/specific_heat_capacity_table.html

The above site is yet another list of specific heats, which is something I had to create myself while trying to find the specific heats of my materials.