# Heat Capacity of a Calorimeter

In calorimetry it is often desirable to know the heat capacity of the calorimeter itself rather than the heat capacity of the entire calorimeter system (calorimeter and water). The heat (q) released by a reaction or process is absorbed by the calorimeter and any substances in the calorimeter. If the only other substance in the calorimeter is water, the following energy balance exists:

q = qcal + qw

where qcal is the heat flow for the calorimeter and qw is the heat flow for the water.

Both of these individual heat flows can be related to the heat capacity and temperature change for the substance.

qcal = Ccal ?T

qw = Cw
?T

where Ccal is the heat capacity of the calorimeter and Cw is the heat capacity of the water. Because the water and calorimeter are in thermal equilibrium, they both have the same temperature and thus ?T is the same for both. The consequence is that the heat capacity of the entire system (C) is the sum of the heat capacities for the individual components.

C = Ccal + Cw

The heat capacity is an extensive property; that is, the heat capacity depends upon the amount of substance present. The calorimeter exists as a fixed unit, thus its heat capacity is a fixed value. The amount of water in the calorimeter, however, can vary, and thus the heat capacity of the water can vary. When dealing with variable amounts of material, one often prefers to use an intensive measure of the heat capacity. One common intensive version of the heat capacity is the specific heat capacity (s), which is the heat capacity of one gram of a substance.

 sw = Cw mw

Because the mass of water (mw) and the specific heat capacity of water are both known, one can readily calculate the heat capacity of the water. The joule (J) is defined based upon the specific heat capacity of water:

sw = 4.184 J oC-1 g-1

Overall one can write

C = Ccal + sw mw

Quantity Symbol Unit Meaning
heat q J Energy transfer that produces or results from a difference in temperature
temperature T oC or K Measure of the kinetic energy of molecular motiom
temperature change ?T oC or K Difference between the final and initial temperatures for a process
mass m g Amount of material present
heat capacity C J oC-1 or J K-1 Heat required to change the temperature of a substance one degree
specific heat capacity s J oC-1 g-1 or J K-1 g-1 Heat required to change the temperature of one gram of a substance one degree

### Experiment

Objective:

• Determine the heat capacity of the calorimeter (Ccal).

Approach:

• Use the heating element to transfer a known amount of heat to the calorimeter system.
• Observe the temperature of the system before and after the heating process.
• Calculate the change in temperature for the system.
• Calculate the heat capacity of the entire calorimeter system.
• Use the mass of water and the specific heat capacity of the water to calculate the heat capacity of the water.
• Calculate the heat capacity of the calorimeter.

In this experiment, the heating element is set to operate for 5 seconds, during which time the heating element will transfer a total of 100 kJ of heat to the calorimeter.

Perform the experiment using one of the three options for the mass of water in the calorimeter. After choosing the mass of water, be sure to reset the calorimeter.

To begin the experiment, record the initial temperature, and select the "Start" button to begin the heating process. When the heating process is finished, record the final temperature and calculate the heat capacity of the system.

After running a simulation, it is necessary to reset the system before running another simulation.

 Mass of Water   500. g 1000. g 1500. g

### Contributors

09:57, 2 Oct 2013

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This material is based upon work supported by the National Science Foundation under Grant Number 1246120