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The “bucket launch” is a fantastic experiment you can do if you have access to liquid nitrogen. See the video below:
Depending upon conditions, I have observed the bucket to launch anywhere from 80 to 160 feet high. For reference, the clock tower you see in the video is 80 feet tall.
To conduct this experiment, I filled a plastic 2L Coke bottle about one-third full with liquid nitrogen and sealed the bottle. The sealed bottle was then placed upright in a pan of room temperature water that was placed on a hard surface. After placing a 5-gallon plastic pail over the soda bottle and pan of water, I quickly moved far away to watch the results.
The liquid nitrogen in the bottle vaporized as it gained energy from the water. Obviously, the pressure in the bottle went up as a result of the buildup of nitrogen gas. The pressure increased to the point where the bottle could no longer contain the gas, and the bottle exploded. (Several online reports indicate that Coca-Cola bottles fail under pressures of about 10 atmospheres). The energy released in the explosion was sufficient to launch the 5 gallon pail high into the air.
I have used this experiment to discuss limitations of the ideal gas law. Using the ideal gas law, the temperature of the nitrogen gas inside the bottle just prior to the explosion can be calculated using:
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Where P is pressure, V is volume, n is moles of gas, R is the gas constant
(0.0821 L atm mol-1 K-1) and T is temperature. The bottle is usually filled with 670 mL (one third of 2 L) of liquid nitrogen. Using the density of liquid nitrogen (0.81 g mL-1) and the molar mass of nitrogen (28 g mol-1), it is found that 670 mL of liquid nitrogen is about 19 moles of nitrogen:
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Using Equation 1, a temperature of 24 K is calculated for the gas just prior to explosion (assuming a little over half of the liquid is vaporized, V= 2 L and P = 10 atm). Of course this calculated temperature makes no sense, since liquid nitrogen boils at 77 K at 1 atm pressure. Certainly the liquid increases in temperature after it changes to a gas. In fact, the liquid itself must increase in temperature as it boils. This is because liquids boil at higher temperatures when subjected to higher pressures: the boiling temperature of nitrogen at P = 10 atm is 105 K. Clearly, the 24 K temperature predicted by the ideal gas law shows that its use is not appropriate for an analysis of this experiment.
There are reasons why the ideal gas law fails under these conditions. The ideal gas law is only useful at relatively high temperatures and low pressures. But in the bucket launch experiment, the pressure is quite high and the temperature is quite low.
The van der Waals equation of state yields a better estimate of the temperature of the nitrogen just prior to explosion. In contrast to the ideal gas law, the van der Waals equation takes into account the fact that real gas molecules take up space and also experience attractive and repulsive forces. The van der Waals equation is:
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In the equation above, a and b are correction factors that take into account the facts that gas molecules have volume (b) and experience attractive and repulsive forces (a). For N2, a = 1.41 atm L2 mol-2 and b = 0.0391 L mol-1. Rearranging the van der Waals equation for temperature, gives:
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Using the van der Waals parameters (a and b) for N2, P = 10 atm, V = 2 L and n =10 mol, a temperature of 90 K is calculated for the temperature of the gas just prior to explosion: a more sensible result. It is notable that this calculated temperature is fairly consistent with the boiling point of nitrogen at 10 atm (105K).