  A detailed study of the transverse momentum distributions of charged
particles produced in proton - proton collisions at LHC energies is presented.
This is done using a thermodynamically consistent form of the Tsallis
distribution. All variables used are thermodynamical and in particular, the
temperature $T$ follows from the standard thermodynamic definition as being the
derivative of the energy with respect to the (Tsallis) entropy. The momentum
distribution of the final state particles obtained describe the transverse
momentum distributions very well. The values of the parameters are determined
from measurements by the ALICE, ATLAS and CMS collaborations and are discussed
in detail. In particular, the Tsallis parameter, $q$ is found with consistent
values for all the transverse momentum distributions despite large differences
in kinematic regions and shows a slight increase with beam energy, reaching a
value of 1.15 at 7 TeV. It is concluded that the hadronic system created in
high-energy p - p collisions can be seen as obeying Tsallis thermodynamics.
