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Equation 1 · Part 3 · AI Datacenter Power and Cooling in 2035: Scenarios, Signals, and Falsifiable Predictions

=

COPCarnot=ThotThot−Tcold,\mathrm{COP}_{\mathrm{Carnot}} = \frac{T_{\mathrm{hot}}}{T_{\mathrm{hot}} - T_{\mathrm{cold}}},
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

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, COPCarnot=ThotThot−Tcold\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…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.