  Recently, a viable varying speed of light (VSL) model has been proposed to
solve various late-time cosmological problems. This model has one free
parameter, $b$, to characterize the time variation of the speed of light as a
function of a scale factor, $c = c_0 a^{b/4}$. Time variation of various
physical constants and quantities are also given by different powers of scale
factor as a function of $b$. Both the sign and the magnitude of this parameter
are generally arbitrary. One can constrain the value of this free parameter,
$b$ from cosmological observation. However, we might be able to theoretically
determine the sign of this parameter by using the general second law of
thermodynamics of the black hole. Any value of $b$ satisfies the generalized
second thermodynamics laws of the black hole except the astrophysical black
holes. The positive values of $b$ are required when the pair-production charge
of the black hole contributes to entropy changes.
