Amount and rate of heat transfer using iron spheres and liquid nitrogen

by Dean J. Campbell, Bradley University, Peoria, Illinois

A previous post described how solid spheres with well-defined sizes can be used to illustrate the differences between the quantities of heat energy transferred in calorimetry and rates at which the energy is transferred.¹ Given two samples of spheres of the same mass and composition, the sample with the smaller spheres has a greater surface area. In that post connecting surface area and calorimetry, the solid spheres were placed in water, and the change in temperature of the water was used to study the transfer of heat energy. A related approach, described here, was inspired by an experiment found online called PH 235 Heat Capacity Experiment with Vernier Software Logger Pro² with additional data provided by the American Institute of Physics Handbook.³ The heat energy associated with the conversion of liquid nitrogen to gas can be studied by adding iron spheres to liquid nitrogen in an open bottle and observing the rate of liquid mass decrease as it converts to gaseous nitrogen.⁴      

N₂ (l) → N₂ (g) 

Iron was the metal selected for this work because it is very Earth-abundant and has low toxicity. The iron spheres can be used multiple times, improving the sustainability of these activities. Iron is ferromagnetic, enabling its movement into, within, and out of activities to be potentially controlled by magnets.⁵ In our planet’s oxidizing atmosphere, the iron spheres will eventually form rust on their surfaces. However, the iron spheres do not necessarily need to be rusty to achieve success in liquid nitrogen experiments, as heat from the spheres will boil the nitrogen in either case.

The supplies required for the calorimetry experiment include:

• Force sensor assembly and means to collect the force data - The masses involved in these measurements far exceed the range of a typical laboratory balance, but larger masses can be measured using a Vernier Dual Range Force Sensor connected to a Vernier LabQuest2 system. The force sensor is attached to a ring stand and oriented vertically. A horizontally aligned rigid plastic panel is affixed to the tip of the sensor with a screw. A layer of thermally insulating material such as cardboard or polystyrene foam is placed on top of the panel. The liquid nitrogen experiment is run on top of the insulated panel.
• Empty 500 mL soda bottles with funnels - The bottles should be marked by permanent markers at the 250 mL level by adding 250 mL of water and then draining. To each bottle a widened tornado tube is added, followed by a short funnel made from a 500 mL soda bottle.
• Balance to measure the mass of the spheres
• Six ½ inch iron spheres (12.7 mm diameter, ~50 g) and an equivalent mass of small rusty iron BB shot (4.3 mm diameter) in lightweight containers such as plastic weighing boats
• Liquid nitrogen and insulated gloves
• Thermometer to measure the temperature of the room

Figure 1 shows the Vernier force sensor assembly with the force sensor vertically oriented and supporting a plastic panel, which in turn supports a weigh boat with rusty iron spheres and a bottle with its funnel. For visual clarity, the bottle in this picture contained water rather than liquid nitrogen.

fig_1_setup.jpg

Figure 1. Vernier force sensor assembly for iron spheres and liquid nitrogen calorimetry experiment with the force sensor vertically oriented and supporting a plastic panel, which in turn supports a weigh boat with rusty iron spheres and a bottle with its funnel.

Before each trial, the LabQuest module was set to take force readings every 0.2 seconds and was set to graph time on the x-axis and force on the y-axis. The room temperature was measured with a thermometer. 250 mL of liquid nitrogen was poured through a funnel into a soda bottle (filled to the marker line). While wearing insulated gloves, the plastic soda bottle was moved onto the Vernier force sensor platform near the center of the plastic panel. Before starting the data collection, a weigh boat of iron spheres was placed on the panel near the bottle. The green arrow icon on the LabQuest screen was pressed to begin data collection. The force pushing down on the sensor slowly decreased as the liquid nitrogen slowly boiled away into the gas phase. After about ten seconds, the iron spheres were swiftly dumped from their weigh boat into the boiling liquid nitrogen and the empty weigh boat was placed back on the panel. The force on the sensor decreased much more quickly as the room temperature iron lost heat to boil the liquid nitrogen more vigorously. The vigorous boiling continued until the iron cooled down to the boiling point of liquid nitrogen. The LabQuest acquisition ran ten seconds past the end of the vigorous boiling of liquid nitrogen. After the measurement run was complete, the insulated gloves were used to remove the bottle containing the liquid nitrogen and the spheres from the plastic panel. The bottle contents could be emptied into a metal container for the liquid nitrogen to evaporate and the spheres to be recovered. Before another trial was run, the plastic panel was removed from the force sensor, warmed by running under warm water, and then allowed to dry.

The data from the LabQuest were moved to LoggerPro and then into Excel. A representative graph of force as a function of time is shown in Figure 2. The graph was scaled so that all of the data points were present and spanned as much of the vertical space available as possible. The graph initially had relatively little noise and a slow overall change in force, corresponding to the liquid nitrogen gently boiling in the bottle. The graph then became much noisier with a much more dramatic change, which corresponded to the iron spheres being added to the bottle and causing more rapid boiling of the liquid nitrogen as the spheres shed heat. After this, the graph had relatively little noise and a slow overall change in force, corresponding to the iron spheres cooling to the boiling point of the liquid nitrogen (77 K) and the remaining liquid nitrogen in the bottle returning to a gentle boil.

The two regions of the graph corresponding to gentle boiling appeared as two lines that are nearly parallel to one another, Figure 2. The vertical distance between the two lines could be found by extending the lines (e.g., with a ruler) and finding where they intercept a common vertical axis (e,g., in the middle of the noisy region). The difference between the y-values of these intersection points gave the difference in force from boiling away liquid nitrogen as the spheres cooled from room temperature to 77 K.

fig_2_liquid_nitrogen_force_curve.jpg

Figure 2. Force measurement curve for adding room temperature iron spheres to liquid nitrogen.

The force difference values in Newtons was multiplied by 101.97 to find the mass change in grams. These grams of nitrogen were converted to moles by dividing by 28.02 g/mol, and then these moles of nitrogen were multiplied by the heat of vaporization of nitrogen (5577J/mol) to yield the Joules required to boil the nitrogen. Assuming that the heat used to boil the nitrogen is equal to the heat released by the iron spheres, the average heat capacity of the iron over the range of room temperature to the boiling point of liquid nitrogen was found by dividing the heat in Joules by the mass of the iron and the temperature change of the iron in Kelvin.

For example:

• 0.20 Newton difference x 101.97 = 20 g N₂ boiled
• 20 g N₂ / 28.02 g/mol = 0.71 mol N₂ boiled
• 0.71 mol N₂ boiled x 5577J/mol N₂ boiled = 4000 J heat absorbed by liquid N₂ 
• 4000 J heat absorbed by liquid N₂ = 4000 J heat released by the cooling iron spheres
• 4000 J / (50 g x (297 K – 77 K)) = 0.36 J/(g x K) for the average heat capacity of iron in this temperature range

The measured iron heat capacity could be compared to literature sources of heat capacity at various temperatures. The heat capacity of iron is 0.449 J/g x K at 298 K, but decreases as temperature decreases.³ One approach to acquiring the literature value was to plot heat capacity as a function of temperature on paper, then cut out the region under the curve over the range from 77 K to 298 K. The area of this region under the curve could be compared to a known rectangular region of the paper by comparing masses of the paper cutouts (a technique known as cut-and-weigh method). Use of this technique and the data in “PH 235 Heat Capacity Experiment with Vernier Software Logger Pro” yielded an average heat capacity of iron over this temperature range of 0.35 J/(g x K).²

Another calculation of interest was estimating the volume of nitrogen gas produced by heat transferred from the iron spheres. Using the average value of 0.35 J/(g x K), cooling 50 g of iron at 298 K to the boiling point of nitrogen at 77 K removed 3.9 kJ of heat from the metal. Since the heat of vaporization of nitrogen is 5.586 kJ/mol, this gave 0.69 mole or 19 g of nitrogen boiled (comparable to the 20 g measured from the data in Figure 2). Using the ideal gas law, the 0.69 mole of nitrogen gas produced by the boiling would have had a volume of 17 L at 298 K and 1 atm pressure.

Many heterogeneous chemical and physical processes are surface-area dependent; that is, the processes proceed more quickly when there is increased contact between reactive phases. A number of demonstrations have been published that illustrate this concept.^6-8 To use this calorimetry experiment to connect surface area and rate of heat transfer, samples containing 50 g of fewer larger iron spheres were compared to 50 g samples of more but smaller iron spheres. The quantity of liquid nitrogen boiled by the iron did not vary greatly between large and small sphere samples, as they were all 50 g, but the rate at which the liquid nitrogen boiled away differed greatly. In these experiments, samples containing fewer larger spheres boiled liquid nitrogen vigorously for longer time periods (because it took longer for them to transfer heat through their lower surface area) than samples containing more but smaller spheres.

To conclude, when iron spheres at room temperature are added to liquid nitrogen, the nitrogen boils as heat is transferred in from the iron, which can be studied with experiments which measure the mass lost by the boiling liquid nitrogen. The amount of liquid nitrogen boiled depends on the amount of heat transferred, which depends on the mass of the iron added. However, the rate at which liquid nitrogen boils depends on the surface area of the iron in contact with the liquid nitrogen.  

Safety

Proper personal protective equipment such as goggles should be used, ESPECIALLY considering vertically rising vapor plumes can be produced. Avoid spilling liquid nitrogen on clothing. Avoid skin contact and wear insulating gloves while working with the liquid nitrogen or working with objects that have been cooled by liquid nitrogen. Always wash your hands after completing the activities.

Acknowledgements

We thank the authors of the PH 235 Heat Capacity Experiment with Vernier Software Logger Pro experiment for inspiration for this work. We thank Kayla Lippincott, Thomas Kuntzleman, Khitab Dar, Cassidy Kraft, Bozana Lojpur, Audrey Stoewer, and Abe Yassin for assistance with this and similar projects involving iron spheres. This work was supported by Bradley University and the Mund-Lagowski Department of Chemistry and Biochemistry with additional support from the Illinois Heartland Section of the American Chemical Society. The material contained in this document is based upon work supported by a National Aeronautics and Space Administration (NASA) grant or cooperative agreement. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the author and do not necessarily reflect the views of NASA. This work was supported through a NASA grant awarded to the Illinois/NASA Space Grant Consortium.

References

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