Hi, I need help with results part. See attached the Lab. I completed all steps, see attached word document, and need help to complete results part. Results1. Write a paragraph that explains what your graphs show. Be specific. What results can you come upwith based on your graphs? Discuss the rate of temperature change during the experiment for eachcup (mix before and mix after).2. Which cup of coffee lost more heat to its surroundings ? Was it the cup that ended up cooler at theend?Results part should include follow for consideration:Clear description of the data for each Graph/Table/Chart and supporting calculation. Concise description of what changed, how much it change and when the changes happened.
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From reading the articles and the procedures of the labs, we have all come to
the hypothesis that Mr. Bergstrom’s coffee will remain warmer if the milk is added first.
This makes sense because of Newton’s Law of Cooling which states that the rate of
heat transfer between an object and its surroundings is proportional
temperature difference between them. According to the article “The History of the
Cooling Law”, research showed that “the cooling process embeds two different
phenomena, thermal radiation and heat transfer by contact”(2). By reading the
procedures from the lab, we know that the Law of Cooling in this specific lab is caused
by heat transfer since adding the milk (a cool liquid) to the coffee (a hot liquid) causes
the temperature of both liquids to become a temperature between the initial
temperatures of the coffee and milk. Adding the milk first will probably cause the
coffee to cool down faster because “Erxleben found that the cooling rate is not
exactly proportional to the temperature difference with the air, and that at higher
temperatures the cooling process is quicker than an exponential law”(4).
Ghoreishi et al. 2
1) Pull out materials (4 styrofoam cups, 1 graduated cylinder, 1 thermometer, 1
2) Measure 160mL of water into 2 of the styrofoam cups and mark where the water
goes up to.
3) The other two cups need to measure 40 ml of cold water.
4) Immediately after measuring the cold water add 160 ml of hot water into one of
the cups which you have previously marked where 160 ml measures.
5) Do this for both coffee cups
6) Immediately measure the temperature of the cold water and coffee cups.
7) Add cold water to coffee number one.
8) Then stir with thermometer and time for 12 minutes.
9) Measure the temperature of the cold water you did not mix, the temperature of
coffee number one.
10) Measure the temperature of coffee number one, coffee number two, and the cold
water you did not mix every 30 seconds.
11) After the 12 minutes have elapsed add the cold water to coffee number two.
Measure for 30 seconds and compare the temperature to the final temperature of
coffee number one.
Ghoreishi et al. 3
Mixed Before Initial
Mixed Before Final
Coffee Initial After
Coffee Final After
Ghoreishi et al. 4
Milk Initial After
Milk Final After
Mixed After Final
Theoretical Ti Before
Theoretical Qlost Before
Qlost Mixed Before
Qlost Total Before
1. Theoretical Ti Before = (4* Coffee Before + Milk Before)/5
(4 * 69+19)/5 = 58.2 ~ 59
2. Theoretical Qlost Before in J = 200*4.186*(Mixed Before Initial – Theoretical Ti
200*4.186*(60-59) = 837.2 J
Theoretical Qlost Before in cal = 200*(Mixed Before Initial – Theoretical Ti Before)
200*(60-59) = 200 cal
3. Qlost Mixed Before in J = 200*4.186*(Mixed Before Final – Mixed Before Initial)
200*4.186(50-60)= -8372 J
Qlost Mixed Before in cal = 200*(Mixed Before Final – Mixed Before Initial)
200*(50-60) = -2000 cal
4. Qlost Total Before in J = Theoretical Qlost Before + Qlost Mixed Before
837.2 + -8372 = -7534.8 J
Qlost Total Before in cal = Theoretical Qlost Before + Qlost Mixed Before
200 + -2000= -1800 cal
5. Percent Error = | (Mixed Before Initial – Theoretical Ti Before)/ Theoretical Ti
| (60 – 59)/59 | = 1.69% ~ 2%
Ghoreishi et al. 5
Qlost Before Mix
Theoretical Tf After
Theoretical Qlost After
Qlost Total After
1. Qlost Coffee in J = 160*4.186*(Coffee Final After – Coffee Initial After)
160*4.186*(55-72) = -11385.92 J
Qlost Coffee in cal = 160*(Coffee Final After – Coffee Initial After)
160*(55-72) = -2720 cal
2. QMilk in J = 40*4.186*( Milk Final After – Milk Initial After)
40*4.186*(20-19) = 167.44 J
QMilk in cal = 40*(Milk Final After – Milk Initial After)
40*(20-19) = 40 cal
3. Qlost Before Mix in J = Qlost Coffee +QMilk
-11385.92 + 167.44 = -11218.48 J
Qlost Before Mix in cal = Qlost Coffee +QMilk
-2720 + 40 = -2680 cal
4. Theoretical Tf After = (160*Coffee Final After+40+20)/200
(160*55+40*20)/200 = 48 C
5. Theoretical Qlost After in J = 200*4.186(Mixed After Final – Theoretical Tf
200*4.186(48-48) = 0 J
Theoretical Qlost After in cal = 200*(Mixed After Final – Theoretical Tf After)
200*(48-48) = 0 cal
6. Qlost Total After in J = Qlost Coffee + QMilk + Theoretical Qlost After
-11385.82 + 167.44 + 0 = -11218. 48 J
Qlost Total After in cal = Qlost Coffee + QMilk + Theoretical Qlost After
-2720 + 40 + 0 = -2680 cal
7. Percent Error = | (Mixed After Final – Theoretical Tf After)/Theoretical Tf After |
| (48 – 48)/48 | = 0%
Ghoreishi et al. 6
Lab: The Coffee Dilemma
NEWTON’S LAW OF COOLING: The
rate of heat transfer between an object and
its surroundings is proportional to the
temperature difference between them.
Example: A chunk of ice will warm up and
melt more quickly in a room that is 25ºC
(77ºF) than it will in a refrigerator that is
THE STEFAN-BOLTZMANN LAW OF RADIATION: The rate of heat lost by radiation is
proportional to the fourth power of the object’s temperature on the Kelvin scale.
Example: You and a cow find yourselves magically floating in outer space. There is no air, so you don’t
lose heat through convection. You don’t touch the cow, so you don’t lose heat through conduction.
BUT, you will lose heat through radiation. The cow’s body temperature is higher than your body
temperature, so the cow loses heat more quickly by giving off infrared waves. The cow would show up
more brightly on a night vision camera than you would.
MR. BERGSTROM’s’S DILEMMA [the “problem” of the experiment]
Mr. Bergstrom is preparing his boiling hot coffee at the beginning of his free block. He is just about to
add some milk when there is an earthquake drill. He estimates that he will be gone for 12 minutes, and
he wants the coffee to be as hot as possible when he returns. There is no microwave nearby so don’t
think about reheating it!
What should he do? Should he add the milk now OR leave the milk on the table in the milk
carton and then add it when he returns? Which method will result in the hottest coffee at the
Prompt for Cooling article
Focusing on Sections 2, 3, 4, 6, 7 and 9 of the paper, analyze and outline the understanding of Newton’s
Law of Cooling throughout history and identify the ideas that relate to our experiment.
What is your hypothesis?
Styrofoam coffee cups, hot water dispenser full of hot water (pretend it is coffee), small cups of cold
water (pretend they are cartons of milk), graduated cylinder, thermometers, stopwatch, container for
carrying hot water from the dispenser to your table.
Guidelines for the procedure:
● Mr. B likes to drink 160 ml of coffee, and he adds 40 ml of milk to it.
● Your experiment should have two parts – one in which you add the milk first, and one in which you
add the milk later.
● You must record the temperature every 30 seconds for twelve minutes (the time that Mr. B is away
from the coffee). You will have at least four people in your group, so distribute data taking jobs
o Take an initial temperature of all four cups and then mix the first coffee and milk at t = 0
seconds. Start timing as soon as you mix the coffee and milk in the “mix” cup and then take
the equilibrium temperature at t = 30s.
o At the end of the 12 minutes, mix the second coffee and milk. Wait 30 seconds and then take
the final temperatures of both mixes at the exact same instant!
● BE SUPER CAREFUL not to tip the cups over. This happens a lot when you have a thermometer
sitting in a Styrofoam cup. If you spill, you must start over!! FROM THE BEGINNING! AHHHH!
● It is hard to measure hot water in the graduated cylinder very quickly (and it’s easy to burn yourself).
You can pre-measure with tap water and mark the 160 ml level on the cups so you can avoid using
the graduated cylinder with the hot water.
Data – in addition to the temperature readings
1. Set up two pieces of graph paper/excel with the same temperature scale that goes from 0ºC to the
maximum temperature that you recorded. Put the time on the x-axis and the temperature on the
y-axis. The two pieces of graph paper should have the exact same
● On the first graph, plot the temperature of the tea that had the milk
added at the beginning. There should only be one line.
● On the other graph, make two separate lines, one for the tea and one
for the milk. The graph should have one final point to show the
temperature after mixing. It should look sort of like the graph to the right.
2. For the mix before the 12-minute break
● Find the theoretical temperature after the mix at 30s (Theoretical Ti Before)
● Find the theoretical heat lost after the mix at 30 s (Theoretical Qlost Before)
● Find the measured heat lost as the mix sits for 12 minutes (Qlost Mixed Before)
● Find the total heat lost after the mix sits for 12 minutes (Qlost Total Before)
3. For the mix after the 12-minute break
● Find the measured heat lost as the coffee sits for 12 minutes (Qlost Coffee)
● Find the measured heat lost as the milk sits for 12 minutes (Q Milk)
● Find the measured total heat lost as the two cups sit for 12 minutes
● Find the theoretical temperature after the mix at 720s (Theoretical Tf After)
● Find the theoretical heat lost after the mix at 720 s (Theoretical Qlost After)
● Find the total heat lost after the mix sits for 12 minutes (Qlost Total After)
4. Calculate the percent error of the theoretical temperatures compared to the measured temperatures
1. Write a paragraph that explains what your graphs show. Be specific. What results can you come up
with based on your graphs? Discuss the rate of temperature change during the experiment for each
cup (mix before and mix after).
2. Which cup of coffee lost more heat to its surroundings? Was it the cup that ended up cooler at the
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