  State functions play important roles in thermodynamics. Different from the
process function, such as the exchanged heat $\delta Q$ and the applied work
$\delta W$, the change of the state function can be expressed as an exact
differential. We prove here that, for a generic thermodynamic system, only the
inverse of the temperature, namely $1/T$, can serve as the integration factor
for the exchanged heat $\delta Q$. The uniqueness of the integration factor
invalidates any attempt to define other state functions associated with the
exchanged heat, and in turn, reveals the incorrectness of defining the entransy
$E_{vh}=C_VT^2 /2$ as a state function by treating $T$ as an integration
factor. We further show the errors in the derivation of entransy by treating
the heat capacity $C_V$ as a temperature-independent constant.
