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Equation 1 · Part 6 · How AI Datacenter Power and Cooling Actually Work

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Q˙=m˙ cp ΔT\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

The physical reason liquid cooling becomes necessary at all is straightforward: air has a volumetric heat capacity roughly one four-thousandth that of water, so once a rack’s heat density crosses roughly 20–30 kW, moving enough air through the rack to hold a safe temperature rise requires impractical airflow velocities and fan power. The heat-removal budget for a cold plate loop follows directly from the sensible-heat relation: Q˙=m˙ cp ΔT\dot{Q} = \dot{m}\, c_p\, \Delta T. where Q˙\dot{Q} is the heat to be removed (watts), m˙\dot{m} is the coolant mass flow rate, cpc_p is its specific heat, and Δ\Delta T is the temperature rise the coolant is allowed across the cold plate. This is the one relationship every cooling-loop…

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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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