Thermal expansion data are used to study the uniaxial pressure dependence of the electronic-magnetic entropy of Ba(Fe(1-x)Co(x))2As2. Uniaxial pressure is found to be proportional to doping and, thus, also an appropriate tuning parameter in this system. Many of the features predicted to occur for a pressure-tuned quantum critical system, in which superconductivity is an emergent phase hiding the critical point, are observed. The electronic-magnetic Grüneisen parameters associated with the spin-density wave and superconducting transitions further demonstrate an intimate connection between both ordering phenomena.