A high heat capacity for the exhaust gas means energy is wasted on heating the exhaust, instead of being used to generate thrust.
CO2 has a much higher heat capacity than steam does, so the exhaust of your methane rocket (which is 1/3 CO2 and 2/3 steam) will have lower temperature (and thrust) than a hydrogen rocket (with only steam in the exhaust gas) if the mass flux for both rockets is identical.
The gases with lowest heat capacities are monatomic and diatomic, so a good rocket fuel tends to have low average molecular weight exhaust.
Author: Fred Senese firstname.lastname@example.org
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Last Revised 02/15/10.URL: http://antoine.frostburg.edu/chem/senese/101/thermo/faq/print-rocket-fuel.shtml