The author has shown previously that the first law of thermodynamics must be modified for materials with negative thermal expansion and for auxetic materials. In this paper, those earlier results have been developed and improved and a paradox stemming from the previous findings has been solved. It is shown that in thermodynamic equations, the motive force of the process must be written on the left-hand side and its effect must be written on the right-hand side. Consequently, the first law of thermodynamics for heat exchange and compression has different signs. This result is of importance for the entire field of thermodynamics. ► The first law of thermodynamics for auxetic materials needs modification. ► Equation describing a compression does not follow from equation of heat transfer. ► Motive force of the process must be written on the left-hand side of the equation.