  The magnetic insulator copper pyrazine dinitrate comprises antiferromagnetic
spin-1/2 chains that are well described by the exactly solvable one-dimensional
Heisenberg model, providing a unique opportunity for a quantitative comparison
between theory and experiment. Here, we investigate its thermodynamic
properties with a particular focus on the field-induced quantum phase
transition. Thermal expansion, magnetostriction, specific heat, magnetization
and magnetocaloric measurements are found to be in excellent agreement with
predictions from exact Bethe-Ansatz results as well as from effective field
theory. Close to the critical field, thermodynamics obeys the expected quantum
critical scaling behavior, and, in particular, the magnetocaloric effect and
the Gr\"uneisen parameters diverge in a characteristic manner. Apart from
realizing a paradigm of quantum criticality, our study instructively
illustrates fundamental principles of quantum critical thermodynamics.
