Revealing QCD thermodynamics in ultrarelativistic nuclear collisions

We show that the mean transverse momentum of charged hadrons, $\langle p_t \rangle$, in ultrarelativistic heavy-ion collisions is proportional the temperature of the quark-gluon plasma from which particles are emitted. We introduce an effective hydrodynamic description of the system created in a relativistic heavy-ion collision to relate experimental data on $\langle p_t \rangle$ and charged-particle multiplicity to the thermodynamic properties of the quark-gluon plasma created in experiments. We find that Large Hadron Collider (LHC) data on Pb-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV is compatible with a deconfined medium with entropy density $s=20 \pm 5$~fm$^{-3}$ and speed of sound $c_s^2=0.24 \pm 0.04$ at a temperature $T=222\pm 9$~MeV, in agreement with lattice calculations. We identify the main sources of theoretical error in the extraction of these quantities from heavy-ion data.