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edit approved May 29, 2022 at 16:01

The operating temperature of the reactor puts an upper limit of $T_t$, above which your fuel elements melt and you (briefly) get a liquid core NTR. Again, not all exhaust species will be created equal here, because their various chemistries at ~3000K±500K~3000 K ± 500 K require various different protective covers around the fuel elements to prevent (or at least limit) corrosion, and those protective layers will have different melting points and thermal properties and so on.

That just leaves you with $M_w$, and which ever way you slice it, water molecules are going to be about 10 times heavier than plain old H2H₂, and when your exhaust gasses are at the same temperature that water is just going to be travelling slower and hence the rocket's I_sp is going to be lower.

Temp  C02 H20 CH4 CO  Ar
2800K 283 370 606 253 165
3000K 310 393 625 264 172 
3200K 337 418 644 274 178 
3500K 381 458 671 289 187

Temperature	CO₂	H₂O	CH₄	CO	Ar
2800 K	283	370	606	253	165
3000 K	310	393	625	264	172
3200 K	337	418	644	274	178
3500 K	381	458	671	289	187

The universe in general, and the outer solar systemSolar System in particular, is just absolutely chock full of water, just lying around, ready for the taking. More or less. It is commonplace, energetically easy to harvest, relatively straightfowardstraightforward to store, given its density and the lack of need for compression or refridgerationrefrigeration or worries about tiny molecules escaping your grasp (sure, you've got to keep it liquid, but you do have a nuclear reactor on your spaceship). And just because the I_sp is low, that doesn't mean that the engine power is low too... the same number of watts are going into the exhaust, and that means high thrust. Its a different use-case to an H2H₂-fuelled NTR, to be sure, but it is still a very handy one.

The operating temperature of the reactor puts an upper limit of $T_t$, above which your fuel elements melt and you (briefly) get a liquid core NTR. Again, not all exhaust species will be created equal here, because their various chemistries at ~3000K±500K require various different protective covers around the fuel elements to prevent (or at least limit) corrosion, and those protective layers will have different melting points and thermal properties and so on.

That just leaves you with $M_w$, and which ever way you slice it, water molecules are going to be about 10 times heavier than plain old H2, and when your exhaust gasses are at the same temperature that water is just going to be travelling slower and hence the rocket's I_sp is going to be lower.

Temp  C02 H20 CH4 CO  Ar
2800K 283 370 606 253 165
3000K 310 393 625 264 172 
3200K 337 418 644 274 178 
3500K 381 458 671 289 187

The universe in general, and the outer solar system in particular, is just absolutely chock full of water, just lying around, ready for the taking. More or less. It is commonplace, energetically easy to harvest, relatively straightfoward to store, given its density and the lack of need for compression or refridgeration or worries about tiny molecules escaping your grasp (sure, you've got to keep it liquid, but you do have a nuclear reactor on your spaceship). And just because the I_sp is low, that doesn't mean that the engine power is low too... the same number of watts are going into the exhaust, and that means high thrust. Its a different use-case to an H2-fuelled NTR, to be sure, but it is still a very handy one.

The operating temperature of the reactor puts an upper limit of $T_t$, above which your fuel elements melt and you (briefly) get a liquid core NTR. Again, not all exhaust species will be created equal here, because their various chemistries at ~3000 K ± 500 K require various different protective covers around the fuel elements to prevent (or at least limit) corrosion, and those protective layers will have different melting points and thermal properties and so on.

That just leaves you with $M_w$, and which ever way you slice it, water molecules are going to be about 10 times heavier than plain old H₂, and when your exhaust gasses are at the same temperature that water is just going to be travelling slower and hence the rocket's I_sp is going to be lower.

Temperature	CO₂	H₂O	CH₄	CO	Ar
2800 K	283	370	606	253	165
3000 K	310	393	625	264	172
3200 K	337	418	644	274	178
3500 K	381	458	671	289	187

The universe in general, and the outer Solar System in particular, is just absolutely chock full of water, just lying around, ready for the taking. More or less. It is commonplace, energetically easy to harvest, relatively straightforward to store, given its density and the lack of need for compression or refrigeration or worries about tiny molecules escaping your grasp (sure, you've got to keep it liquid, but you do have a nuclear reactor on your spaceship). And just because the I_sp is low, that doesn't mean that the engine power is low too... the same number of watts are going into the exhaust, and that means high thrust. Its a different use-case to an H₂-fuelled NTR, to be sure, but it is still a very handy one.

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created Feb 26, 2021 at 10:19

Starfish Prime

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To copy the key part of this answer (and this related earlier answer)... an important figure of merit in a rocket engine is the "characteristic velocity":

$$c_* \propto \sqrt{\frac{T_t}{M_w}}$$

where $T_t$ can be taken to be the exhaust temperature, and $M_w$ is the molecular weight of the gas species in the exhaust.

(The "proportional" bit is doing some work here as not all exhaust species are created equal... the heat capacity ratio is an important factor that the author of the older answer mentioned, and I don't doubt there are others).

The operating temperature of the reactor puts an upper limit of $T_t$, above which your fuel elements melt and you (briefly) get a liquid core NTR. Again, not all exhaust species will be created equal here, because their various chemistries at ~3000K±500K require various different protective covers around the fuel elements to prevent (or at least limit) corrosion, and those protective layers will have different melting points and thermal properties and so on.

This 1990 paper by Zubrin lists some other potential NTR fuels and their expected specific impulses at various core temperatures, and you can see these tally reasonably well with the above relation.

Temp  C02 H20 CH4 CO  Ar
2800K 283 370 606 253 165
3000K 310 393 625 264 172 
3200K 337 418 644 274 178 
3500K 381 458 671 289 187

But to counter your main complaint:

there is almost no point in using anything but hydrogen as propellant for a solid-core NTR... common volatiles such as water [are] worse than even low-performance chemfuel.