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Equation 8 · Part 6 · How AI Datacenter Power and Cooling Actually Work

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Q˙=m˙cpΔT\dot{Q} = \dot{m} c_p \Delta T
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What this part means

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

Its job in the formula

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

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

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the article section

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