What does this equation mean?

Analysis. What Odense does not settle is why heat reuse is common in Denmark and rare almost everywhere else, and thermodynamics supplies at least part of the answer independent of policy. A heat pump’s maximum possible efficiency at converting electrical work into delivered heat is set by the Carnot limit, $\mathrm{COP}_{\mathrm{Carnot}} = \frac{T_{\mathrm{hot}}}{T_{\mathrm{hot}} - T_{\mathrm{cold}}}$. 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 $\mathrm{COP}_{\mathrm{Carnot}}$ = 348/(348-303) $\approx$ 7.7 ; lifting a warmer waste stream at 45 °C (318 K) to the same 75 °C supply gives $\mathrm{COP}_{\mathrm{Carnot}}$ $\approx$ 348/(348-318) = 11.6 . Real ammonia heat pumps of the kind used at Odense achieve only a fraction of the Carnot figure once irreversibilities are accounted for, but the ratio between the two cases survives that discount: a waste stream that leaves the datacenter fifteen degrees warmer needs meaningfully less electricity per unit of district heat delivered. Because ASHRAE’s own facility water classes are organised explicitly by the maximum temperature a design tolerates, W17 through W45 and W+ [ 9 ] , the choice of cooling architecture and the choice of facility water class are not separable from heat-reuse economics — they are decided upstream of it, years before any district-heating operator gets a phone call.