= Mantle potential temperature
{title2=$T_p$}
The <temperature> a parcel of <mantle> material would attain after a reversible <adiabatic process> bringing it to a specified reference pressure, without changing its composition or phase assemblage. It removes the compressional contribution when comparing sources at different depths. Within one phase and with depth $z$ positive downward, the <adiabatic process> gives the gradient is $dT/dz=\alpha gT/c_p$, so
$$
T_p=T(z)\exp\left(-\int_0^z\frac{\alpha(s)g(s)}{c_p(s)}\,ds\right).
$$
Absolute <temperature> is used inside this formula. Recovering a source $T_p$ from erupted <magma> also requires accounting for melting, <latent heat>, ascent and <fractional crystallization>; an eruption temperature is not automatically a <mantle potential temperature>.
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