# Tidal Acceleration

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.

General Relativity. A few short lectures by Avi Rabinowitz, which give a good introduction to the ideas of GR.

A ring of particles free fall in a non-uniform gravitational field.

Particles free fall along lines that pass through the center of the large mass.

# Exploding Liquid Nitrogen

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?

Solution to Question 1

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.

Solution to Question 2

Question 3: What is the change in temperature of the water due to the heating of the nitrogen?

Solution to Question 3

Question 4: What is the pressure inside a 2L volume when 50 ml of liquid nitrogen is changed to a gas at 300K?

Solution to Question 4

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?

Solution to Question 6

Question 7: What is the amount of water displaced by the explosion?

# Spectrogram Rachele Gilmore

A spectrogram of Rachele Gilmore singing “The Doll’s Song,” from the 2009 Metropolitan Opera production of “Tales Of Hoffman”. It shows the last 30 seconds of this song. A-flat above high C is marked on the spectrogram at the end of this video.

I found out about Rachele Gilmore from this most excellent article.
Rachele Gilmore’s 100 MPH Fastball

# Make a Spectrogram

You can make a spectrogram using Audacity. It is free, open source software for recording and editing sounds. Audacity is available for Mac OS X, Microsoft Windows, and GNU/Linux. I am using the PC version running on Windows 7. It can be downloaded from

http://audacity.sourceforge.net/

After starting it for the first time you will probably need to change the Input Device to (“What U Hear”) and Input Channel to (Mono) as shown in the diagram below.

I am using the audio captured from this YouTube video.
Rachele Gilmore – Met Debut – Olympia

Here is how to record the audio.
Start playing the video and then click on the record button in Audacity.
Click the stop button to end the recording.

Now click the Fit Project button. This will show the entire recording.
To see the Spectrogram view of the recording, click the drop down menu next to Audio Track and select Spectrogram.

You should have something that looks like this.

We can increase the resolution of the displayed spectrogram by selecting under Edit, Preferences, Spectrograms, Window size 4096. The default is 256. What this does is take the sample rate 44,100 Hz and divides it by 4096. The result is about 10.8 Hz. So the vertical scale goes up in steps of 10.8 Hz.

To zoom the vertical scale, hover the mouse pointer over the vertical scale, left click and drag down, release.

Now zoom the horizontal scale, left click highlight a selection and then click the Fit Selection button.

The final result looks like.