Again I ask: what is this lost mass doing?
Answer: it is expanding (i.e. combusting), just like the propellant, P, in my above examples.
We see that P in the example of a cannon expands between 2 masses (the cannon & the cannonball) in order to create recoil, so in the case of a rocket we have mass 1, the rocket; P, the expanding propellant, and...
What, exactly?
Where is mass 2?
Find mass 2 & understand the Truth...
Markjo: anyone can google 'adiabatic exchange' & 'adiabatic transfer' to understand the terms are interchangeable.
But, as I correctly predicted, quibbling over definitions is your last hope of 'victory', so it is what you are doing.
When rocket fuel is combusted within the combustion chamber, it is then ejected out through the engine nozzles as high speed super heated exhaust gas particles. As in my previous example, if 500kg of fuel is combusted within the engine every second, then obviously 500kg of high speed super heated exhaust is also created every second - there is NO mass lost during this process.
It seems to me, that you're not comprehending that the 500kg of fuel that is combusted every second, retains the same weight when it is ejected out of the engine nozzles, ie. the newly created exhaust weighs exactly the same as the fuel that it formerly existed as - all that's happened, is that this 'parcel of mass' has changed its form from a liquid with 500kg of mass, to exhaust particles with 500kg of mass.
I hope you're not going to say that a mass of 500kg travelling at hypersonic speed does not have a large amount of momentum? And remember that this 500kg parcel of mass is being created and ejected out of the system every second.
How can you not understand that this 500kg of exhaust (formerly 500kg of fuel), which is created every second, is your 'mystery' mass 2?
You seem quite happy that the system comprising a cannon and a cannonball, causes the cannon to recoil due to the momentum of the cannonball travelling in the opposite direction, yet you can't see that the system comprised of a rocket and its fuel, acts in exactly the same way, whereby the momentum of the exhaust (mass 2) causes the rocket to be propelled (recoiled) in the opposite direction?
So the relevant conservation of momentum equation looks like this -
M(rocket)
V(rocket) = -
M(exhaust)
V(exhaust)
Just to recap, it's the 500kg of exhaust (formerly 500kg of fuel) being ejected out of the 'rocket system' every second, that is mass 2.
This is EXACTLY the same as the cannonball (mass 2) being ejected out of the 'cannon/cannonball system' and the medicine ball (mass 2) being ejected out of the 'man/medicine ball system'.