New thermoaynamic fundamentals for vertical pneumatic conveying are proposed with derivation based strictly on mass conservation and continuum concept. For a I-D, vertical, steady gas-solid flow, these new mass and energy balances allowed the derivation of a new nondimensional energy factor containing the pressure drop. This energy factor correlated quite well with the difference between the inlet gas velocity and solids terminal velocity when tested against high-pressure, 15-m-high, vertical pneumatic transport data from Institute of Gas Technology. The energy factor was also checked against atmosphetic-pressure data of the 5-m lift line of the Pennsylvania State University The new energy factor covers quite well both the atmospheric- and high-pressure sets of data (923 tests) including two heights, lean- and dense-phase transports, several pipe diameters, broad and narrow particle-size distributions, and different materials. The dissipation terms in gas-solid flow were also clearly identified.