Though different materials have different dependences of entropy on internal energy, the derivative of entropy with respect to energy will be the same for any two materials in thermal equilibrium with...Though different materials have different dependences of entropy on internal energy, the derivative of entropy with respect to energy will be the same for any two materials in thermal equilibrium with each other. If we had left off Boltzmann’s constant in the definition of entropy, the dimensions of temperature would be that of energy.