Specific Heat; “coffee cup” calorimetry

In this exercise, you will use “coffee cup” calorimetry to measure the heat flow between a
cool liquid (water in Parts 2 and 3, oil in Part 4) and hot water when they are mixed. In Part 2 and
3, you will verify that the amount of heat lost by the hot water is equal to the amount of heat gained
by the cool water, i.e. you will verify the First Law of Thermodynamics/Conservation of Energy. In
Part 4, you will determine the specific heat of the oil.
Introduction:
Heat is a form of energy that can flow into or out of materials and cause them to either
change their temperature or change their state or phase from a solid to a liquid or to a gas. In the SI
system, heat is measured in units of Joules like all forms of energy. Another non-SI unit of heat still
in common usage is the calorie. The Laws of Thermodynamics describe how and why heat flows
from place to place.
The specific heat capacity (or “specific heat” for short) of a material expresses how much
its temperature changes when it is heated or cooled. The higher a material’s specific heat, the more
heat it takes to generate the same temperature change. Put another way, a material with a higher
specific heat changes temperature less with the same amount of heating or cooling. If a material
with a total mass m and a specific heat c absorbs a total amount of heat Q, its temperature will
change by T according to the following formula:

In this experiment, we will express heat in units of Joules, mass in units of grams, and temperature
changes in units of degrees Centigrade (oC). Consequently, specific heat is expressed in units of
“Joules per gram per degree Centigrade” or J/goC.
The Zeroth Law of Thermodynamics defines temperature as the property that governs
whether two bodies will exchange heat when they are in thermal contact, i.e. not isolated from one
another by distance or by an insulating material like styrofoam. The Zeroth Law says that objects
at different temperatures will exchange heat. When they reach the same temperature, heat exchange
stops and they are said to be in thermal equilibrium. The Second Law of Thermodynamics
states that heat naturally flows from higher temperatures to lower temperatures. As a result, a hotter
object cools and a cooler objects warms. Temperature change and/or phase change will continue
until thermal equilibrium is achieved. When two bodies exchange heat, the First Law of
Thermodynamics (otherwise known as the Law of Conservation of Energy) states that the amount
of heat lost by the hotter object must be equal to the amount of heat gained by the colder object.

An experimental technique called calorimetery uses the principles of thermodynamics to
determine heat flow in physical processes. A simple “coffee cup” calorimeter can be constructed
using a Styrofoam cup and a thermometer. The Styrofoam is a good insulator that prevents heat
flow between the interior of the cup and the surrounding air; heat energy stays inside the
calorimeter. The calorimeter is filled with water. Another object at a different temperature is
dropped into the water. The water in the calorimeter cup and the object exchange heat until they are
at the same temperature. The specific heat of water is a well-known quantity, 4.18 J/goC. By
measuring the temperature change of the water with a thermometer, the amount of heat the object
exchanged with the water can be determined from eq. (1). By the First Law of Thermodynamics eq.
(2), any heat gained/lost by the water must have come from/gone into the object that was dropped
into the water. From the object’s mass and temperature change, eq. (1) can be used again to
determine its specific heat as well.
Procedure
Materials Needed:
Three Styrofoam coffee cups that can hold at least one cup of fluid, a measuring cup,
adhesive tape, some popsicle sticks or coins, some corrugated cardboard or a sheet of Styrofoam
(you don’t mind cutting up), a cooking or meat thermometer with a temperature range between
100o
F/40oC and 200o
F/95oC (a digital thermometer seems to work best), an indoor thermometer, a
stove or microwave oven, vegetable oil, and tap water.
If you don’t already have a cooking thermometer, purchase an inexpensive cooking/meat
thermometer from the grocery store or borrow one from a friend/family/neighbor. A meat
thermometer works very well for this experiment, since it has a needle-like probe tip. If your
indoor thermometer can’t be moved, it is best to do the experiment in the same room it is mounted
if you can.
Part 1: Constructing the Coffee-Cup Calorimeter and Preliminary Setup

  1. Take one of the Styrofoam cups and tape either the coins or popsicles sticks to the sides. If you
    are using popsicle sticks, break them into 1 inch lengths first. Place this cup into a second cup.
    The coins/sticks act as spacers and keep a thin layer of air between the two cups. An unmoving
    layer of “dead” air is a very good insulator; this is why double-paned windows are so energy
    efficient. Finish off by wrapping a strip of adhesive tape around the space between the top of
    the two cups, to seal off the air between them. Between the air layer and the Styrofoam, your
    calorimeter should be well-insulated.
  2. Now, take the corrugated cardboard/Styrofoam sheet and cut out a circular piece for a lid. If
    you use cardboard you should use corrugated cardboard; thin cardboard will not work nearly as
    well as an insulating lid. Cut the lid about an inch wider in diameter than the top of the coffee
    cup. You will need to either punch or cut a hole into the center of the lid to insert your
    thermometer. Keep the hole as small as possible; a tight hole will both improve insulation and
    help hold your thermometer firm. You can keep the thermometer in the lid throughout the
    experiment. If you use a glass cooking thermometer, be careful when inserting it into the lid
    and transferring it.
  3. Measure out 1/3rd of a cup (79 mL) of water into the third Styrofoam cup. Using a small knife,
    pencil, pen, etc., mark the top of the water level on the inside of the cup. Pour out the water.
    Repeat this process with a 1/4th of a cup (59 mL) of water. You will be using this cup to
    measure out portions of hot water to pour into the room temperature water (or oil) inside the
    calorimeter. By pre-marking the water levels, you can do this more speedily, which will
    minimize heat loss from the hot water.
  4. Set a large container of tap water and the oil in whichever room you plan to perform the
    experiment. Let them sit out in the open for at least a couple of hours. If you can, let them sit
    out overnight. This is to ensure that both are at “room temperature”. Throughout the
    experiment, we will be referring to the room temperature water as the “cool” water.
  5. Make sure that you read the following instructions completely before you perform the
    experiment. At various stages, either speed or patience will be very important. You will need
    to be prepared before you start each part if you want good data.
  6. Once you are ready to begin your experiment, record the temperature in the room where you
    kept the water and oil.
    Part 2: Verifying the First Law (equal amounts of hot and cool water)
  7. Measure out 1/3rd of a cup (79 mL) of cool water into your calorimeter. Be as precise about this
    measurement as you can.
  8. Now you will need some hot water. You can boil water in the measuring cup with your
    microwave (assuming it is microwave safe) or put a big pot of water on the stovetop and boil it.
    If you use the stovetop, keep the water at a slow rolling boil while performing the experiment.
    If you use the microwave, stop the microwave as soon as you can see a strong boil begin in the
    measuring cup.
  9. Transfer enough of your boiled water into the third Styrofoam cup up to exactly the 1/3 cup/79
    mL mark. If you have to, use a spoon to remove excess until you’re lined up perfectly with your
    previous mark. Be careful not to burn yourself, but don’t take too long either.
    Warning: Water in a microwave can occasionally “superheat”, meaning that it remains liquid
    even though it is actually hotter than its normal boiling point temperature. Superheated water
    can look placid, but once you pour it or put a spoon in it, etc. it explosively boils and sprays
    everywhere. This is a very very rare occurrence, but something anyone who uses a microwave
    regularly to boil water should be aware of. If you’re heating water and it seems to be taking
    way too long to boil, it may be superheating. Just let it cool down and try again.
  10. Put the lid over the cup of hot water. Insert the thermometer into the lid. The tip of the
    thermometer needs to be in the water. Wait for the temperature reading on the thermometer to
    stabilize; the temperature on the thermometer shouldn’t be changing more than 1oC in 30
    second. Record the temperature of the hot water. A space is provided for both o
    F and oC
    measurements. If you measure in o
    F, you will convert to oC later.
  11. Remove the thermometer from the lid and swish the end of the thermometer in your original
    supply of cool water or under a flow of cold water from your sink for a few seconds. You are
    trying to quickly drop its reading down near that of the cool water supply. Don’t take too long
    with this; you don’t want your hot water to cool off too much.
  12. Now, quickly remove the lid from the hot water’s cup and pour the hot water into the
    calorimeter cup. Quickly place the lid on the calorimeter cup and reinsert the thermometer in its
    hole. Swish the cup around to mix the two waters. The thermometer reading should rise
    quickly at first, stabilize, and then start slowly dropping (as the contents of the calorimeter begin
    losing heat through the sides and top of the cup into the surrounding). Determine the highest
    temperature reading that the thermometer reaches before it starts dropping again. Record this
    temperature in your Data Sheet as the equilibrium temperature between the hot and cool water.
  13. Pour out the contents of the calorimeter.
    You now have the data you need to perform the calculations for this part of the exercise. Steps 14-
    20 outline how to perform those calculations. If you prefer, you may save the calculations for later
    and collect the data for the other two parts of the lab instead.
  14. Convert the initial and equilibrium temperature readings from degrees Fahrenheit to degrees
    Celsius. If you recorded in Celsius originally, convert to Fahrenheit instead. Note: For all
    subsequent calculations, you will be using the Celsius temperatures only.
  15. Determine the mass of both the hot water mh and the cool water mc you poured into the
    calorimeter. The density of water is close to 1 gram per milliliter, so the volume of water in
    milliliters equals its mass in grams.
  16. Determine how much the temperature of the cool water changed Tc, from its initial temperature
    (“room” temperature) before you put it in the calorimeter to its final equilibrium temperature
    after it was mixed with hot water.
  17. Determine the temperature change of the hot water |Th| from your initial measurement of its
    temperature just before you poured it into the calorimeter and its final equilibrium temperature
    after mixing with the cool water. Although the temperature of the hot water dropped (and
    therefore Th is properly a negative number), record this change in temperature as a positive
    number (we will ignore minus signs for this).
  18. Using eq. (1), calculate the heat Qc that was absorbed by the cool water in the calorimeter.
    Show your work for this calculation.
  19. Using eq. (1), calculate the heat |Qh| that was lost by the hot water. Show your work for this
    calculation.
  20. Calculate the % difference between the heat lost and the heat gained. Assuming that the
    calorimeter is well-insulated and the First Law of Thermodynamics is correct, these should be
    very similar and your % diff should be close to zero.
    Note: If you find that your % diff is greater than 20%, you should probably either recheck
    your calculations or redo the experiment. If the large % difference persists, your calorimeter
    may not be well-insulated enough or you may be taking too much time transferring the hot
    water into the calorimeter cup after you have finished measuring its temperature.
    Even though your calorimeter should be well-insulated, it is inevitable that some of the heat
    that flowed out of the hot water was lost to the outside air instead of going into the cool water.
    Thus, the heat gained by the cool water should always be a little less than the heat lost by the hot
    water. If you find after calculation that your cool water gained more heat than the hot water
    lost, it is also strongly advised that you redo the experiment.
    Part 3: Verifying the First Law (unequal amounts of hot and cool water)
  21. Repeat the Steps 7-19, but this time use ½ a cup (118 mL) of cool water in the calorimeter cup
    and 1/4th of a cup (59 mL) of hot water.
    Part 4: Determining the Specific Heat of Oil
  22. Repeat Steps 7-12, this time using 1/3 of a cup of vegetable oil (olive, canola, peanut, etc.) for
    your cool liquid in the calorimeter and 1/3 of a cup of hot water. If you can safely do so, you
    should try to stir the calorimeter contents after pouring them together. Remember, oil and water
    don’t naturally mix. Stirring should help the system reach equilibrium with much greater
    efficiency.
  23. Find the specific heat of the oil you used online. A Google search should find it without too
    much trouble. Be specific about what kind of oil you used: vegetable oil, canola oil, olive oil,
    peanut oil, etc. Different oils have different specific heats.
    Note: Make sure that you find the specific heat of your oil in units of Joules per gram degree
    Celsius to be consistent with the units of the other quantities in this lab. Check to see which
    units the website is using before writing your value down.
    If the specific heat you find is listed in units of Joules per gram degree Kelvin, that is fine.
    A temperature change expressed in degrees Centigrade is the same as the temperature change
    expressed in degree Kelvin.
    Another unit commonly used to measure heat is the calorie; the websites you find may well
    give specific heats in units of calories/goC. If the website is using calories instead of Joules,
    you can convert from calories to Joules using the following conversion factor:
    1 calorie = 4.184 Joules.
    Record which particular type of oil you used and its actual specific heat coil,act (J/goC) in the
    Data Sheet.
  24. Find the “density” doil of the oil that you used online and record. Density is defined as the ratio
    of a material’s mass versus its volume (read Chapter 9, p 174 for more information). The
    density you record needs to be in units of grams per milliliter.
  25. Multiply the density of the oil (in grams per milliliter) by the milliliters of oil used to determine
    the mass of the oil, in grams.
  26. Determine the temperature change of the hot water. Determine the temperature change of the
    oil.
  27. Assume that all the heat lost by the hot water was gained by the oil. Using eq. (1) and the data
    you’ve gathered, find the “experimental” value of specific heat coil,exp for the oil. You will need
    to rearrange eq. (1) to solve for coil,exp. Note that the specific heat of oil will be determined by
    the mass, heat absorbed, and temperature change of the oil.
  28. Calculate the % error between the oil’s actual specific heat, which you found online in Step 23,
    and the specific heat you determined experimentally in Step 27.
    Answer the questions in Part 5.
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