How fast could 1,767 cubic feet of fusion fuel propel a starship? I'm designing a starship that could go to Alpha Centauri in under 15 years. My design goes at a top speed of 0.5c. Assuming the fuel is in gaseous form, could this provide enough energy to propel it? (It needs to speed up, but not noticeably, since there's already an artificial gravity ring.)
 A: Given the OP's numbers, the payload will not attain relativistic speeds unless it is quite small.  To show this, we'll make a bunch of unrealistically optimistic assumptions and show that the mass of the payload must end up being pretty small.
We will assume that the entire fusion energy of the fuel is converted into the KE of the payload.  Of course, this is entirely unrealistic;  in reality, a significant portion of the reaction energy will be imparted to the fuel itself, and thermodynamics will impose further limits.In comments, the OP specified a tank of hydrogen gas at 10 psi.  Let's assume a temperature of 20 K, so that it's as dense as possible but still gaseous.  Using the ideal gas law, we can estimate the number of hydrogen atoms in this tank as $N = 2\frac{PV}{kT}$, which works out to be about $N \approx 2.5 \times 10^{28}$.  (The factor of two comes from the fact that there are 2 hydrogen atoms per molecule in the gas.)
Now, we'll assume that we've mastered deuterium-tritium fusion, and have managed to breed tritium in the reactor for this purpose.  This reaction releases about 8.8 MeV of energy per hydrogen atom fused.  If this energy all goes into the KE of the payload (and again—I cannot stress this enough—this is an unrealistic assumption), the payload will get an energy of $K \approx 3.3 \times 10^{16}$ J. If the object is to be travelling at $0.5c$ with this amount of kinetic energy, then its Lorentz factor will be $\gamma = 1/\sqrt{1 - 0.5^2} = 2/\sqrt{3}$, and so its rest mass will be
$$
K = (\gamma - 1) m c^2 \quad \Rightarrow \quad m = \frac{K}{(2/\sqrt{3} - 1) c^2}
$$
which works out to $m \approx 2.5$ kg.  I doubt that you could build a tank to hold the hydrogen with this mass, let alone an artificial gravity ring.
In reality, the situation is much, much worse that this;  the exponential properties of the rocket equation mean that you'd actually need far, far more fuel than I've mentioned here to get a payload of 2.5 kg up to $0.5c$.  A more detailed calculation would require details about the rocket's exhaust velocity, reaction mass, reaction type, reactor efficiency, and probably some stuff I haven't mentioned to boot.  The above calculation is mainly to show that the provided numbers don't even get you close to the speed of light for a reasonably sized crewed spacecraft.
