# How to Graph the Heat Capacity of a Calorimeter

Written by john brennan
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A calorimeter measures the heat released or absorbed by a reaction. Calorimetry is an important tool in chemistry, and chemists often work with devices called bomb calorimeters. For home or classroom experiments, however, a coffee cup calorimeter is sufficient to make rough measurements. Before using your calorimeter, you need to calibrate it with a reaction that supplies a known amount of heat.

Skill level:
Moderate

### Things you need

• Four styrofoam cups with lids
• Two thermometers
• Stirrer
• Water
• Microwave oven
• Graph paper
• Calculator

## Instructions

1. 1

Fill a beaker with cold water. Insert both thermometers and measure the temperature of each to make sure they record the same temperature. If for some reason they do not, take the difference between the two and correct all future measurements with the thermometers by this difference. For example, if one thermometer measures 10.1 degrees C and the other measures 10.3 degrees C, add -17.7 degrees C to all your measurements with the first thermometer for the remainder of the experiment.

2. 2

Make two calorimeters by inserting one styrofoam cup into another and covering it with the lid.

3. 3

Warm up some water in a microwave for about 20 seconds and record its temperature.

4. 4

Pour 50 millilitres of cold water into one calorimeter and 50 millilitres of warm water into the other. Cover both calorimeters with the lids and measure the temperature in each with the thermometers. Record the temperature at one minute intervals for a total of four minutes. (You can check time using a watch or your microwave clock.)

5. 5

Pour the warm water into the cold water calorimeter and measure the temperature at one-minute intervals for a total of three minutes.

6. 6

Plot your data on graph paper, using time as the x-axis and temperature as the y-axis. You should have data points that form three separate lines: the cold-water calorimeter, the warm-water calorimeter and the mixed water temperature.

7. 7

Use the graph for the mixed-water temperature to do a linear regression, where you will find the values of m and b for the equation y = mx + b. Y in this equation will be temperature while b will be the y-intercept. The link under the Resources section of this article provides a simple calculator you can use to find m and b.

8. 8

Use the equation you derived in the last step to calculate the mixed water temperature at X = 4 minutes.

9. 9

Subtract the cool water temperature at 4 minutes from the mixed water temperature and multiply this difference by 4.18 and 50 to get the amount of heat gained by the cool water.

10. 10

Subtract the temperature of the mixed water from the temperature of the warm water at 4 minutes and multiply by 50 and 4.18 to get the amount of heat lost by the warm water.

11. 11

Subtract the heat gained by the cool water from the heat lost by the warm water and call this value X. Next, divide X by the difference in temperature between the cool water at 4 minutes and the mixed water at 4 minutes. This final answer is the heat capacity of your cool-water calorimeter.

#### Tips and warnings

• This process uses a graph to find the heat capacity of the coffee-cup calorimeter. As you can see, however, it's not as precise as it could be. For one thing, this procedure doesn't ask you to find the error or uncertainty in your calculations. In science, a measurement without an uncertainty is meaningless because no measurement can be infinitely precise.

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