We predict that the mean transverse momentum of charged hadrons $langle p_trangle$ rises as a function of the charged-particle multiplicity in ultracentral nucleus-nucleus collisions. We explain that this phenomenon has a simple physical origin and represents an unambiguous prediction of the hydrodynamic framework of heavy-ion collisions. We argue that the relative increase of $langle p_t rangle$ is proportional to the speed of sound squared $c_s^2$ of the quark-gluon plasma. Based on the value of $c_s^2$ from lattice QCD, we expect $langle p_trangle$ to increase by approximately $18$ MeV between 1% and 0.001% centrality in Pb+Pb collisions at $sqrt{s_{rm NN}}=5.02$ TeV.
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