The heat capacity of the entire calorimeter system (C) is the sum of the heat capacities of the calorimeter (Ccal) and all of the substances in the calorimeter. Although water is the most frequently used liquid, it is possible to employ a liquid other than water in the calorimeter. In this example, suppose the calorimeter contains ethanol. The heat capacity of the entire calorimeter system is thus
C = Ccal + CEtOH
The heat capacity of the ethanol (CEtOH) depends upon how much ethanol is in the system. It is therefore more convenient to replace CEtOH with the specific heat capacity of ethanol (sEtOH) and the mass of ethanol (mEtOH).
C = Ccal + sEtOH mEtOH
Experimentally one knows the mass of ethanol used in the experiment, and one can measure the heat capacity of the entire calorimeter system. This leaves two unknowns, Ccal and sEtOH, in the above equation.
One approach to determining these values is to perform two experiments using two different masses of ethanol. Two equations involving Ccal and sEtOH may then be written. The simultaneous solution of these two equations yields values for Ccal and sEtOH.
A superior strategy for determining Ccal and sEtOH is to make a series of measurements of C at varying values of mEtOH. A plot of C vs mEtOH will yield of straight line with a slope of sEtOH and an intercept of Ccal. This approach has the advantage of using multiple measurements to obtain "average" values of Ccal and sEtOH to reduce the experimental error. In addition, the linearity of the plot is a good diagnostic tool for checking the integrity of both the data and the theory used to generate the working equation.
- Determine the heat capacity of the calorimeter (Ccal).
- Determine the specific heat capacity of ethanol (sEtOH).
- 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 (C).
- Prepare a plot of C vs mEtOH.
- Obtain Ccal and sEtOH from the intercept and slope, respectively, of the line-of-best-fit.
Perform a series of experiments using different masses of ethanol. Prior to each experiment, enter the mass of ethanol (between 300. and 1000. g). Reset the simulation and then perform the virtual experiment. The heating element is set to transfer a total of 50 kJ of heat to the calorimeter.
After each experiment, calculate the heat capacity of the entire calorimeter system (C). Enter the values for C and mEtOH in the "Add Point" fields and click on the "Add Point" button. This data point will be plotted on the graph.
When you have plotted at least four points, click on the "Draw Line" button, and the line-of-best-fit will be plotted and the slope and intercept displayed.
Bear in mind that random error has been added to the simulated data. One consequence of this error is that the points will not all lie perfectly on a line. Another consequence is that the values for C and mEtOH obtained from the linear regression will not be perfectly accurate. Try repeating measurements to see the reproducibility of the data.