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Published equation contexts

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

Why this formula appears here

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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ThotT_{\mathrm{hot}}

Symbol T_hot

ThT_hot is one of the signed contributions combined to compute the quantity on the left.

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TcoldT_{\mathrm{cold}}

Symbol T_cold

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

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Thot−TcoldT_{\mathrm{hot}} - T_{\mathrm{cold}}

Denominator: T_hot - T_cold

The complete quantity below the fraction bar; it must be nonzero for this division.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

Research cited beside this formula

Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

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

Equation 1 · Datacenters

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

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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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