Lab 2 Clairaut’s Theorem

2003 Lab # 2 The Heat of Vaporization of Liquid Nitrogen I. Introduction The object of this experiment is to measure the heat of vaporization per gram (L) of liquid nitrogen. The experimental procedure is quite simple. It consists of carefully placing a known mass of aluminum initially at room temperature into a cup of liquid nitrogen, and measuring the mass of nitrogen that evaporates. We will also determine L by boiling liquid nitrogen with power dissipated by an electrical resistor submerged in the liquid nitrogen. WARNING 1. Liquid nitrogen is very cold, so do not let it, or any object which has been cooled by it, touch you or your clothing in any way. 2. Do not drop anything into the liquid nitrogen. Wear safety goggles at all times. 3. Place the piece of aluminum in the liquid nitrogen slowly, as it will cause the liquid nitrogen to boil rapidly until equilibrium is reached. A piece of string is supplied for this purpose. II. Some Theoretical Details We want to find L, the energy required to change 1 kg of liquid nitrogen (at 77 K, its boiling temperature at one atmosphere pressure) to its gaseous form at the same temperature. In this experiment, you measure the mass MN of nitrogen that converts from liquid to gas as the liquid nitrogen cools a piece of aluminum from room temperature to 77 K. As the aluminum cools, it transmits thermal energy Q to the nitrogen. We then find L from L = Q/MN. The thermal energy Q given off as the aluminum cools can be determined from the known heat capacity of aluminum, which, to make life complicated (but with some interesting physics) varies significantly with temperature. The heat capacity is defined as the ratio of thermal energy absorbed or emitted (dQ) to the corresponding temperature change dT: dQ C(T) = (1) dT If we rearrange the previous equation, we can write dQ = C(T)dT (2) We then integrate both sides of this equation from Ti to Tf and denote the total thermal energy exchanged by Q: Tf Q = ∫ C(T)dT (3) Ti We will provide you with graphical data for C(T) that allow you to find the numerical value of this integral. III. The Experiment You will be provided with an electronic balance that has a sensitivity of ± 0.1 g or better. You’ll also have a stop watch, three Styrofoam cups for storing liquid nitrogen, goggles, and a small aluminum cylinder with a piece of string attached. One cup should be placed inside a second one to improve the thermal insulation properties. The third cup will be for storage of some additional liquid nitrogen. In analyzing the results to find the heat of vaporization of liquid nitrogen, you need to know that the specific heat of aluminum, Cp(T), varies significantly between room temperature and 77K, the temperature at which liquid nitrogen vaporizes under atmospheric pressure. A graph showing the temperature variation of Cp is attached. Note: As you’ll quickly observe, some of the liquid nitrogen evaporates even when the aluminum isn’t put into the liquid. You must somehow account for this “background” evaporation effect in your determination of L. We will leave it up to you and your lab partners to determine the appropriate procedure. You should note, however, that the background evaporation, due to heat leaks through the cups and to heating from the air, does vary considerably depending upon your setup. Hence, your procedure should determine this background evaporation in situ, that is, just before you place the aluminum into the liquid nitrogen and just after the aluminum has come to equilibrium with the nitrogen. Measure how much liquid nitrogen vaporizes when the aluminum cylinder is placed in the liquid. Use the experimental results plus the given information on the specific heat of aluminum, to determine the heat of vaporization per unit mass, L, of liquid nitrogen. Room temperature will probably be ~ 22°C, but you should check this with one of the thermometers provided. If your procedure is working appropriately, you should obtain a result within 10% or so of the value (about 199 J/g) determined in other experiments. Experimental Uncertainties: To get an estimate of the experimental uncertainty to be associated with your results, you should carry out your procedure at least three times and compare the scatter of the results you obtain for L. IV. Another Method of Determining L You can also determine L by providing energy to the liquid nitrogen by passing electrical current through a resistor immersed in the liquid nitrogen. We will provide you with some digital multimeters, wires, and resistors and let you design the procedures for determining L. 2 V. The Report. You will write a formal report giving a complete description of this lab work. Your report should be written for an audience of Physics 34 students who have not yet done this experiment. Your report should include properly-labeled tables of your measurements (including units), sample calculations, including a clear indication of how you accounted for “background evaporation,” and your experimental values for L, including estimates of your experimental uncertainties. Make clear how you arrived at these estimates. In addition, you should compare your measured values for L with both the value obtained in other experiments (approximately 199 J/g) and with the value of L for water. You should give a qualitative discussion of why the value of L for nitrogen is bigger or smaller than that for water. HINT: Find the latent heat of vaporization per molecule in each case. You should also compare the latent heat of vaporization per molecule to other molecular energies (some examples: ionization energies, vibrational energy differences, rotational energy differences). I nternal Energy Capacity of Al 1 0.9 0.8 Cp J/(g-K) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 50 100 150 200 Temperature (K) 3 250 300 350