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By performing heat-capacity, magnetocaloric effect, torque magnetometry, and force magnetometry measurements up to 33 T, we have mapped out the $T\text{\ensuremath{-}}H$ phase diagram of the $S=1/2$ spin dimer compound ${\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}$. We found evidence for field-induced magnetic order between ${H}_{c1}=12.52(2)\text{ }\text{T}$ and ${H}_{c2}=23.60(5)\text{ }\text{T}$, with the maximum transition temperature ${T}_{c}\ensuremath{\sim}2.7\text{ }\text{K}$ at $H\ensuremath{\sim}18\text{ }\text{T}$. The lower transition can likely be described by Bose-Einstein condensation of triplons theory, and this is consistent with the absence of any magnetization plateaus in our magnetic torque and force measurements. In contrast, our measurements uncovered magnetic field irreversibility associated with a symmetric specific heat versus temperature near ${H}_{c2}$ suggesting that the upper transition is first order.

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