Equation 1 · Part 3 · The Physical Plant: Power, Cooling, and Networks in an AI Datacenter

Specific heat capacity

\dot{Q} = \dot{m}\,c_p\,\Delta T = \rho\,\dot{V}\,c_p\,\Delta T,

c_p

What this part means

The heat needed to raise one kilogram of the fluid by one kelvin at approximately constant pressure. Its SI unit is joules per kilogram per kelvin.

Its job in the formula

$c_p$ is an input to the expression that computes the quantity on the left.

Full expressionSpecific heat capacityArticle meaning

The passage around this formula

The rate at which a fluid stream removes heat is $\dot{Q} = \dot{m}\,c_p\,\Delta T = \rho\,\dot{V}\,c_p\,\Delta T$ . with mass flow $\dot{m}$ , specific heat capacity $c_p$ , and the temperature rise $\Delta$ T across the load. What matters for a datacenter is not $c_p$ per kilogram but the volumetric heat capacity $\rho$ $c_p$ , because the room has to physically contain the flow.

Read this part in the article →

Learn the underlying idea

Units describe how a quantity is measured. A valid physical equation must combine compatible dimensions.

Open the illustrated units and dimensions: a formula’s consistency check guide →

See this notation across published equations →

Sources cited in the article section

[4] Emergence and Expansion of Liquid Cooling in Mainstream Data Centers ↗

These citations provide research context; check each source for the exact claim it supports.