When applying the Lorentz transformations of the coordinates of space to different types of volumes such as the volume of a gas and the rational volume between the gas and its molecules in a thermodynamic system, the observer gets contradictory results in the same frame of reference, Although the contradictory results are for different types of volumes, but both types are thermodynamic variables, or in other words, both types have an effect on gas pressure, Thus, the observer gets contradictory results also in the same frame of reference for relativistic pressure, as a result, the Lorentz transformations for different volumes represent a new paradox in special relativity, this paradox is not a mistake in special relativity, but it reveals to us the limits of the special theory of relativity in application, and the reasons for the failure to combine special relativity with thermodynamics.