Nuclear Thermal Rocket

Back when I started the blog Stephen D. Howe said that I should make a page about nuclear thermal rockets (you can see the comment on my home page). So here it is. The way the NTR works is by taking a liquid, usually liquid hydrogen, and heating it inside the space around a nuclear reactor.  This causes it to expand out of the rocket nozzle.  So really, isn’t this what we do when we use nuclear reactors as forms of energy? The big difference is that we are using propellant instead of water. If we are already using this on our planet, why don’t we use it to power space ships?