Calorimetry

Introduction: One material is distinguishable from another by its qualities. How it absorbs and retains heat is one of those qualities.

Theory: Density, elastic modulus, melting point, resistivity and many more are qualities that identify a substance. Many values are virtually the same for a number of materials so to correctly identify that material requires finding its unique set (or at least a subset) of qualities.

Specific heat capacity - c - is a material's ability to absorb and retain heat, given by this equation:

Equation 1 where Q is the amount of heat introduced, m is mass and T is temperature. The c for water is rather high, about ten times that of iron. This means that it takes more energy to heat a mass of water up by a certain amount than for the same mass and temperature gain for iron. Similarly, water will give up more heat while cooling down less than the same mass of iron.

For example, if we introduce hot iron into cold water, obviously the iron will cool and the water will warm. Using conservation of thermal energy:

Equation 2

Qlost is the energy leaving the hot object (negative, as in work done) to warm up the cooler object. Without intervention by an external process (such as a heat pump), heat always flows from hotter to cooler objects. Combining Equations 1 and 2 and specifying the objects only by their initial temperatures:

Equation 3 we see that the two objects will come to a final, common temperature once there is no more temperature differential. In some cases that final, common temperature is the goal of the experiment, but if we know all the masses and temperatures, as well as one specific heat capacity, we can use this hot-added-to-cold technique, known as calorimetry, to find the second c in our quest to identify a substance.

Task:

To identify an unknown substance by at least two of its intrinsic qualities

Equipment:

thermometer water unknown substance calorimeter graduated cylinder Pasco Capstone Interface (PCI)

Procedure:

You will be mixing a hot unknown substance in room temperature water. To make the experiment more interesting, the unknown substance is actually a mixture of 66% copper and 34% something else by mass. While you might be able to isolate one identifying quantity (density or specific heat capacity) from one aspect of this experiment, there could be many substances with said property identical to the unknown. By finding two identifying quantities you can narrow your search and be more positive in your outcome.

Be sure your report includes a clear table using MKS units of the following data:

Mass of water for calorimetry Mass of the metal mixture Initial hot temperature of mixture Initial cold temperature of mixture Final temperature of mixture Mass of mixture for the density calculation if different from above Volume of the mixture

Figure 1

1. Set up the PCI as in Figure 1, observe the progress of the experiment with a table and graph. a. Use the wireless temperature sensor. b. Set your sensor precision for at least three decimal places. 2. Measure the mass of the unknown substance. 3. Measure the mass of the aluminum calorimeter without the hugger, then put the hugger on it.

4. Find the volume of the unknown by displacement in a graduated cylinder. a. One cm3 = 1 ml b. 1 ml of water -> 1 gram 5. Put a known amount of water into the calorimeter and mass it. Measure the water temeprature. 6. Heat the unknown and measure its temperature. a. The hot temperature doesn't have to be very hot: 90oC - 100oC is sufficient. 7. Add the hot unknown substance to the water and wait until the mixture reaches a final, common temperature. The graph will should be pretty flat at this point.

Calculations:

1. Use the mass and volume of the mixture to find its density, then calculate the contribution to that density made by the unknown. 2. Use your data and Equation 3 to find the mixture's specific heat capacity, then calculate the contribution to that specific heat made by the unknown. 3. Isolate the density and specific heat of the unknown in the mixture and use the internet to identify the substance. 4. Be sure to address the uncertainties in your error analysis!