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Equation 4 · How AI Datacenter Power and Cooling Actually Work

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cpc_p

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its specific heat. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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cpc_p

Symbol c_p

its specific heat.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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What the article says around this equation

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 sizing decision in this article reduces to: a facility either raises m˙\dot{m} (bigger pumps, more flow, more pumping power) or accepts a larger Δ\Delta T (which raises the return coolant temperature and can push a heat-reuse exchanger below its useful delivery temperature, discussed below). There is no way around the equation; every design choice downstream is a trade against these three terms.

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