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COPCarnot=348/(348−303)≈7.7\mathrm{COP}_{\mathrm{Carnot}} = 348/(348-303) \approx 7.7

Why this formula appears here

with both temperatures in kelvin. The following is my own illustrative calculation, using representative round numbers rather than any specific project’s measured temperatures, to show how sharply this ratio depends on the lift between the waste-heat source and the district-heating supply it must reach — commonly on the order of 70–80 °C in an established European district-heating network. Lifting a relatively cool waste stream at 30 °C (303 K) to a 75 °C (348 K) supply gives COPCarnot\mathrm{COP}_{\mathrm{Carnot}} = 348/(348-303) ≈\approx 7.7 ; lifting a warmer waste stream at 45 °C (318 K) to the same 75 °C supply gives COPCarnot\mathrm{COP}_{\mathrm{Carnot}} ≈\approx 348/(348-318) = 11.6 . Real ammonia heat…

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Published contexts (1)

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COPCarnot=348/(348−303)≈7.7\mathrm{COP}_{\mathrm{Carnot}} = 348/(348-303) \approx 7.7

Equation 2 · Datacenters

AI Datacenter Power and Cooling in 2035: Scenarios, Signals, and Falsifiable Predictions

This equation gives an approximation: it relates the quantities while allowing an approximation.

with both temperatures in kelvin. The following is my own illustrative calculation, using representative round numbers rather than any specific project’s measured temperatures, to show how sharply this ratio depends on the lift between the waste-heat source and the district-heating supply it must reach — commonly on the order of 70–80 °C in an established European district-heating network. Lifting a relatively cool waste stream at 30 °C (303 K) to a 75 °C (348 K) supply gives COPCarnot\mathrm{COP}_{\mathrm{Carnot}} = 348/(348-303) ≈\approx 7.7 ; lifting a warmer waste stream at 45 °C (318 K) to the same 75 °C supply gives COPCarnot\mathrm{COP}_{\mathrm{Carnot}} ≈\approx 348/(348-318) = 11.6 . Real ammonia heat…

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