[en] CeRhIn₅ is known to show an unusual transition at a critical pressure of ∼15 kbar. Specific-heat data show a gradual change in the zero-field 'magnetic' specific-heat anomaly from one typical of antiferromagnetic (AF) ordering at ambient pressure to one more characteristic of a Kondo singlet ground state at 21 kbar. However, at 15 kbar there is a discontinuous change from an AF ground state to a superconducting ground state, and evidence of a weak thermodynamic first-order transition. Above the critical pressure, the low-energy excitations are characteristic of superconductivity with line nodes in the energy gap, and, at intermediate pressures, of extended gaplessness