# Homework Help: Rocket engine operating in a vacuum

1. Oct 26, 2016

### oobgular

1. The problem statement, all variables and given/known data
So suppose there is a chemical rocket operating in the vacuum of space (assume it's a perfect vacuum). It generates a hot gas with a total enthalpy of h. What's the final speed of the rocket exhaust, in terms of h?

2. Relevant equations
The energy equation seems to be useful here:
h0 = h_exhaust + 1/2v^2 (from my textbook-- it's stated in the middle of a derivation with no explanation, but I assume it's applicable in this case)
h = c_p*T

3. The attempt at a solution
I feel like there isn't enough information to solve the problem accurately, since we are only given h. My first thought was that because it is a perfect vacuum, we can assume the exhaust enthalpy is 0, and so v = sqrt(2*h0)

Not only does that seem too simple, but also I don't think it's reasonable that all enthalpy is lost-- wouldn't that assume T drops to absolute zero? And I thought all molecular movement stops at absolute zero, so how could there still be a flow of gas?

Can someone help me with clarifying this? Thanks!

2. Oct 26, 2016

### Staff: Mentor

A hypothetical ideal rocket nozzle would have indeed the gas leave at "0 K": all particles move in the same direction at the same speed. That would need an infinite nozzle and various other silly things, so real rockets are always just approximations, but you can assume the ideal case here.