  Studies of the Gr\"uneisen ratio, i.e., the ratio between thermal expansion
and specific heat, have become a powerful tool in the context of quantum
criticality, since it was shown theoretically that the Gr\"uneisen ratio
displays characteristic power-law divergencies upon approaching the transition
point of a continuous quantum phase transition. Here we show that the
Gr\"uneisen ratio also diverges at a symmetry-enhanced first-order quantum
phase transition, albeit with mean-field exponents, as the enhanced symmetry
implies the vanishing of a mode gap which is finite away from the transition.
We provide explicit results for simple pseudo-spin models, both with and
without Goldstone modes in the stable phases, and discuss implications.
