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Equation 1 · Part 2 · AI Datacenter Power and Cooling in 2035: Scenarios, Signals, and Falsifiable Predictions

Symbol T_cold

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

What this part means

TcT_cold occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Its job in the formula

TcT_cold occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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