Experiment 10
Objective:
To measure the specific heat (heat capacity) of a selected material or substance
Equipment:
A computer with internet connection, a calculator (The builtin calculator of the computer may be used.), a ruler, a few sheets of paper, and a pencil
Theory:
Although the SI unit for any type of energy is Joule; however, the commonly used units for heat are calorie (cal), kilocalorie (kcal), and Btu.
1cal is the amount of heat that can raise the temperature of 1gr of pure water by 1^{o}C.
{On the average, the best range is from 58.5 to 59.5^{o}C}.
1kcal is the heat that can raise the temperature of 1kg of pure water by 1^{o}C.
British Thermal Unit (Btu):
1Btu is the heat that can raise the temperature of 1lb_{m} of pure water by 1^{o}F.
Definition of Specific Heat:
The specific heat c of a substance is the # of kcal that 1kg of that substance absorbs to warm up by 1^{o}C. The specific heat of water is therefore:
c_{water} = 

because of the way 1cal is defined, or 
c_{water} = 

because of the way 1kcal is defined, or 
c_{water} = 

because of the way 1Btu is defined. 
The specific heat for other materials may be found in physics texts or handbooks.
In this experiment, since mass will mainly be expressed or measured in grams, we will use the unit shown on the right for specific heat. 

On this basis, c_{iron} = 0.108 

Note that in general, metals take less heat for their temperature to increase by a certain amount compared to water; therefore, metals have lower specific heats than water. 
The conversion between calorie and Joule is 1cal = 4.186J. Based on this conversion, The specific heats of water and iron become:
c_{water} = 

c_{iron} = 
Calorimeter
Calorimeter is a thermal device that is thermally insulated from its surroundings. A good thermos jug that can keep hot water for 24 hours is a good calorimeter. A double layer plastic coffee cup with a tight lid may also be used as a calorimeter.
Thermal Worth of a Calorimeter
If the mass M of the inner pot of a calorimeter along with its heat capacity c are known, they can be used in heat balance calculations in different experiments to determine other unknown quantities. If you decide to use a thermos jug as a calorimeter, the effective mass of its inner pot as well as its specific heat are unknown. It is good to know both values; however, knowing just the product of those two values is as good as knowing the individual values. Knowing the product Mc is enough to perform other calculations.
For an object, the product Mc may be defined as its thermal worth. The product Mc is important to be known for a calorimeter because it is not always practical to disassemble a calorimeter and measure the mass of the effective part of its container. The method of finding Mc may be learned from the following example:
Example: A calorimeter contains 100 grams of water at 25.0^{o}C. To measure its Mc, 200 grams of water at 55.0^{o}C is added to it. As a result, an equilibrium temperature of 43.0^{o}C is reached. Find the product Mc of this calorimeter.
Solution: In this problem, the calorimeter and the 100grams of water already in it absorb heat, but the added water loses heat because the added water is initially at a higher temperature. The heat balance equation, may be written as:
Heat gain by [calorimeter + its water] =  Heat loss by the added water.
[(Mc)_{cal} + (Mc)_{water}](43.025.0)^{o}C =  [(Mc)_{ added water}](43.055.0)^{o}C.
[(Mc )_{cal} + 100 * 4.186](18.0) =  [200 * 4.186 ](12.0).
(Mc )_{cal} = 139.5 J/^{o}C.
Procedure:
Use the applet's calorimeter to measure the heat capacity of a substance. Suppose the goal is to measure the heat capacity of copper. Also let the heat capacity of iron be used as known. The experiment will have two parts:
Part 1 is to measure the Mc of the calorimeter by using the known value of the heat capacity of iron. Once the Mc of the calorimeter is determined, it will be used in Part 2 to measure the heat capacity of copper.
Click on the following applet: http://www.chm.davidson.edu/ChemistryApplets/calorimetry/
SpecificHeatCapacityOfCopper.html
Note: In the applet the equation for q_{cal }= C_{cal} ( T_{f}  T_{i} ) has a misprint in it. Please learn the correct form of it before starting. The correct form should read q_{cal }= M_{cal}C_{cal} ( T_{f}  T_{i} ). M_{cal} is missing in the applet. Remember we need to first calculate the product Mc of the calorimeter not just c_{cal} as shown in the applet.
Part 1: Measuring the Mcvalue of the Calorimeter
1. In Part 1 of the applet, you can choose the mass of iron as well as the mass of the water in the calorimeter. Note that the mass of iron must be from 1 to 100 grams and that of water (in the calorimeter) is from 50 to 90 grams. Select a mass for iron and one for water in the specified limits.
2. Click on the "Reset" button. Before clicking on the "Start", you need to write down the initial temperature of the calorimeter from the thermometer. This is also the initial temperature of the water in the calorimeter. Note that each graduation on the thermometer is 0.2 ^{o}C.
3. Click on the "Start" button and wait for thermal equilibrium to be reached. You need to wait about 10 seconds until the thermometer comes to a fixed temperature. Record the final temperature. Read the temperature to your best estimate. Also, note that this final temperature is for the calorimeter, its water, as well as the iron dropped in it. The initial temperature of iron is assumed to be 100^{o}C. The assumption is that the piece of iron is pulled out of boiling water before being dropped in the calorimeter. This guarantees an initial temperature of 100^{o}C or very close to it. Record all values in Table 1 under the "Data Section."
4. Now you have all data to calculate for the Mc of the calorimeter. Perform a calculation similar to the Example above. On the left side, in the example, the mass of water is 100grams. You need to replace that with whatever mass you chose for water in your experiment (applet). The specific heat of water is 1 cal /(gr ^{o}C) or 4.186 J/(gr ^{o}C). On the right side, the added water must be replaced with iron. Apply the mass of iron you chose, and let the specific heat of iron be 0.450J/(gr ^{o}C) as given in the applet. Perform the calculations and solve for the Mc of the calorimeter. Record the calculated value of Mc in Table 1.
5. Now that the Mc of the calorimeter is known, it can be used in Part 2 to find the heat capacity of copper.
Part 2: The main Experiment: Measuring the Specific Heat of Copper
1. Go to Part 2 of the applet. Here again as in Part 1 for iron, the assumption is that you are keeping the copper piece in boiling water for long enough time such that its initial temperature is 100^{o}C. Choose a mass for copper and one for the water in the calorimeter. Reset the applet. Read and record the initial temperature of the calorimeter. Start the applet. The hot copper piece will drop into the calorimeter. Wait long enough for the calorimeter temperature to stabilize. Record the equilibrium temperature.
2. Use the collected data to calculate the specific heat of copper. On the left side you should have the calorimeter and its water as heat absorbers (colder objects). On the right side you should have the copper piece that gives off heat (the hotter object). Solve for c_{copper }. What comes out of your calculation will be your measured value. Then compare that with the accepted value for the specific heat of copper: 0.387J/(gr ^{o}C).
3. Calculate a %error and record all values in Table 2 of the Data Section.
4. Repeat the whole experiment (2 more times) with different choices for masses of water, iron, and copper. Each time you should get the same results for Mc in Part 1, and for c_{copper} in Part 2.
Data:
Given: c_{water} = 4.186 J/(gr ^{o}C) and c_{iron} = 0.450 J/(gr ^{o}C).
Table 1
Trial  Mass of water (grams)  Mass of Iron(grams)  Initial Temp. of Water (^{o}C)  Initial Temp. of Calorimeter (^{o}C)  Initial Temp. of Iron (^{o}C)  Equilibrium Temp. (^{o}C)  Mc
of the Calorimeter
(J/C) 
1  100.  
2  100.  
3  100. 
Measured: c_{copper} = ????
Table 2
Trial  Water Mass grams  Mc of Calrmtr (J/^{o}C)  Mass of Copper(grams)  Initial Temp. of Calrmtr (C)  Initial Temp. of Water (^{o}C)  Initial Temp. of Copper(^{o}C)  Equilib. Temp. (^{o}C) 
c_{copper.} _{ }J/(gr ^{o}C) 
% Error 
1  100.  
2  100.  
3  100. 
Calculations:
Equation: Heat gain by colder object (s) =  Heat loss by hot object (s).
Complete the calculations.
Comparison of the Results:
Conclusion: To be explained by students
Discussion: To be explained by students