This experiment verified that heat is a form of energy and that energy is conserved. For the elemental metals of aluminum, copper, zinc, and lead, our experimental values of the mass specific heat agreed within experimental error with the accepted values. The molar specific heat of these metals ranged from 5.0 ± 0.7 to 8 ± 3 cal/mol•°C. They all agreed with the kinetic theory prediction of Dulong and Petit of about 6 cal/mol•°C.
Given that the Dulong-Petit law holds, our value of the specific heat of a brass sample of 0.093 cal/mol•°C translated into an experimental molecular weight of the alloy of 65 g/mol.
All of the samples had the same mass, to within a gram or so. Yet putting a 100°C sample into about the same amount of water at about the same temperature raised the temperature of the water different amounts. Aluminum had the greatest effect while lead had the least. Qualitatively, this means that aluminum can hold more thermal energy per unit mass than lead can. And this is the meaning of specific heat, reflected in the quantitative values: the specific heat of aluminum is greater than that of lead.
Questions
1. If brass is an alloy of two of these four metals, I would say that those two have to be copper and zinc. Both the molecular weights and the specific heats of all 3 metals are close to each other. But could it conceivably be made of aluminum and lead? First, what would the mixing percentage of the two have to be to get a molecular weight of 65 g/mol? Assume that the ratio of aluminum in such an alloy is x. Then
We would also need
These two ratios are not the same, so brass cannot be made of aluminum and lead.
2. To derive the expression for the specific heat, start with the fact that heat is a form of energy and that energy is conserved. Then
Assume that all of the thermal energy lost from the wet sample (metal plus water droplets starting at Th) is gained by the calorimeter cup (aluminum cup plus water starting at Tc). The final equilibrium temperature of both is Tf. The amount of heat Q transferred to or from a mass m that has a specific heat c over a temperature difference DT is
Then
3. Propagating the uncertainty of the specific heat u{c} (for brass):
Specific heat of a metal,
(Since mw/mh is about 0.5/70, or less than 0.01, compared to specific heats of ~ 0.1, any errors in this part of the calculation will not be a major part of the total calculation, so we can ignore it in calculating u{c}.)
