"Combined Heat and Power" (CHP) or "cogeneration" systems for producing both heat and electric power are generally mature and really can reduce emissions of CO2 compared to other fossil-fuel technologies. But there are two problems with typical discussion of CHP:
(1) Fossil-fuel-based CHP cannot be a long-term solution on climate or energy because they still burn fossil fuels, and therefore still emit a lot of CO2. Reducing that by 20% or even 50% is not enough; we need to take steps that over the next 30-40 years will bring fossil CO2 emissions close to 0.
(2) Efficiency claims for CHP systems are frequently greatly overstated. Heat is lower-quality energy than electricity, and only at high temperatures does it become close to comparable. Efficiency claims for CHP systems that use high-temperature heat are not so far off, but CHP systems that make use of low-temperature waste heat have much lower thermodynamic efficiencies than usually claimed.
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