The energy equations don't care about causation. Expansion from higher than ambient pressure down to ambient pressure through the nozzle yields lower temperature and transfers kinetic energy to the rocket. "Why" is irrelevant to the problem. :-)
But, on a conceptual level, temperature is a measure of the mean kinetic energy of the molecules of the gas. For a given particle in motion, K = 0.5 m v^2. (Kinetic energy is one-half the mass times the velocity squared.)
When gas molecules collide with the walls of the nozzle, the collision is "elastic", and energy is conserved. Thus, kinetic energy of the gas molecules is reduced by the same amount that the kinetic energy of the nozzle (and hence, the rocket) is increased. So, the temperature of the exhaust goes down, and the rocket gets a little extra "push". Work and energy are equivalent, so 1 Joule of energy lost by the gas results in 1 Joule of work done on the nozzle, which is 1 Newton of force applied over a distance of 1 meter.
Ok, let me see if I've got this straight... The thermal energy (heat) is what makes the gas expand, the expanding gas pushing against the nozzle is the mechanism by which the energy exchange takes place. Right?
EXCELLANT ARTICLE Mike! Finally no 'Jerry Irvine bullshit', just straight forward researched answers. Ever notice how Jerry never goes into depth on a topic. He only spouts bits and pieces to come off as knowlegable, but never goes into serious depth. I learned that about Jerry a long time ago ... just a short little man, full of bullshit and promises.
Well any way, I to have the Sutton book, 5th or 6th edition, its in storage along with boxes of my old college books.
What I remember from the book is that a well designed nozzel should be one that is most effectient with mass flow of reactants at a heght of
2/3 of the projected altitude at which that engine/motor is going to operate at.
Also, the reactant exaust leaves the reaction chamber at a cooler temperature due to thermodynamic effects. You see in Brownian motion, a particle has an X, Y, and Z direction of motion. Energy for each drection is E sub n = 1/2KT, where E sub n = Ex, Ey, or Ez, K = Plank's constant, and T = temperature. Now this is from memory, so it might be wrong in formular, but CORRECT in theory.
Now as exhaust leaves the chamber, one of the major E sub n values nearly vanish due the reactants being forced in two ordninant directions. Same way an aerosol can works. The contents are under pressure and have higher heat/temp, then when you press down and release them, they cool down rapidly due to the new directional constraints placed on the contents. The E sub n lost in this process goes into increased kenetic energy in the forced direction, i.e. the exhaust increases its speed, and loses its heat energy.
Nozzels also have to be designed so that the "downstream" exhuast reactants know nothing of what is going on upstream in the exhaust. This is why the expansion of the nozzle occurs. At the throat of the nozzel, the exit speed of the reactants is Mach 1+. Now due to the expansion of the mass flow, the speed of the exhaust increases upwards of 10 fold. Idealy, you would want to expand the mass flow to infinity, but that would require a nozzle the size of infinity ... not going to happen!
I could go deeper into the topic, but I can't remember all the equations, just the theory and principles. I hope this helps!
Please don't give Jerry Irvine a forum. Listen to the people here who have actually done the work and the research ... not Jerry who just copies everyone else, and then claims it to be his own. Sorry Jerry, but I have to tell the truth.
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