An example of tidal acceleration discussed in General Relativity. It shows a ring of particles free falling in a non-uniform gravitational field. Specifically 5 gram dice falling toward a 1000 kg “bowling ball”, time is speed up. The program Universe Sandbox was used in creating this simulation.
I read an article by Rhett Allain. “Exploding Liquid Nitrogen: Where Does the Energy Come From?” This article examines a video of an exploding 2 liter plastic bottle. A small amount of liquid nitrogen, about 50 ml, was poured into the plastic bottle and a cap was screwed on. As the liquid nitrogen changed into a gas the pressure increased and burst the bottle. Specifically, the video shows a capped bottle with liquid nitrogen being dropped into a 32 gallon plastic garbage can filled with water and floating rubber ducks. Shortly after BOOM! The explosion was captured in slow motion video, very cool.
Do NOT attempt to do anything like what is shown in this video. It can be very dangerous. I am not associated in any way with the making of this video. I discovered it form the article mentioned above. Do NOT rely on any information in my blog. I strive for accuracy but the data and my reasoning could be wrong.
This article and video sparked my interest in explosions caused by liquid nitrogen. What impressed me is how a small amount of liquid nitrogen can create such a large explosion. It heats up, turns into a gas, and burst its container. Can the energy associated with the phase change and heating of the gas cause the observed explosion? You cannot always trust what you see on the internet. Maybe there was something else in the garbage can that caused the explosion. Here is one way to find out. What if all the energy transferred into the nitrogen is used to do work lifting the can and water. If the calculated height is one inch I don’t believe, if 10 ft I believe it’s possible. The result of the calculation is 40 ft (see below)
I believe the heating of the nitrogen by about 15 kJ (see below) is enough to cause the work done by the explosion. This thermal energy is converted into work very quickly by the abrupt rupture of the bottle. The pressure that a 2L bottle bursts at is about 160 psi. The amount of work done by the explosion depends on the burst pressure of the bottle not on the gas used. Carbon dioxide gas produced by dry ice would work just as well. Below are questions with answers about the physics related to this video, but first some general properties of nitrogen.
Properties of liquid nitrogen LN2
Boiling point = 77.36K (-195.8°C) (-320.5°F) at one atmosphere
Density = 0.808 g/ml at its boiling point
Latent heat of evaporation = 199 J/g at one atmosphere and 77.36K
Properties of nitrogen gas N2
Specific heat (constant pressure) = 1.04 J/(gK) at 300K
Specific heat (constant volume) = 0.743 J/(gK) at 300K
Gamma (Cp/Cv) = 1.4 at 300K
Temperature of 300K = (27°C) (80°F)
Question 1: Estimate how much energy input by heating was transferred into the nitrogen?
Question 2: Calculate the height of the garbage can and water if all the energy transferred into the nitrogen is used to do work lifting it.
Question 3: What is the change in temperature of the water due to the heating of the nitrogen?
Question 4: What is the pressure inside a 2L volume when 50 ml of liquid nitrogen is changed to a gas at 300K?
Question 5: What is the approximate burst pressure of a 2L plastic bottle?
Source: Air Command Water Rockets
Question 6: Given 50 ml of liquid nitrogen, what is its volume at room temperature and pressure?
Question 7: What is the amount of water displaced by the explosion?
Answer: to be determined