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Equation 8 · Part 5 · How AI Datacenter Power and Cooling Actually Work

=

Q˙=m˙cpΔT\dot{Q} = \dot{m} c_p \Delta T
=

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

Heat reuse imposes a real constraint back onto the cooling-loop design, and it is a direct consequence of the Q˙\dot{Q} = m˙\dot{m} cpc_p Δ\Delta T relation above: a district heating network needs delivery water above some useful temperature (often 60–90°C depending on the network), which is far above what a direct-to-chip loop returns on its own. A heat pump bridges that gap, but every heat pump has a coefficient of performance that degrades as the temperature lift it must perform increases — so a datacenter operator sizing for heat reuse has a genuine incentive to run its internal coolant loop at a higher return temperature than a pure cooling-efficiency design would choose, trading some…

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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.

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Sources cited in the article section

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