  Pressure dependence of longitudinal relaxation time (T$_1$) due to the cell
wall was observed previously at both room temperature and low temperature in
valved Rb-coated refillable $^3$He gaseous cells in \cite{Zheng2}. The
diffusion of $^3$He from measurement cell through a capillary tube to the valve
and the subsequent depolarization on the surface of the valve was proposed to
possibly explain such a pressure dependence at room temperature \cite{Saam}. In
this paper, we investigate this diffusion effect through measurements of T$_1$
with newly designed Rb-coated Pyrex glass cells at 295 K as well as finite
element analysis (FEA) studies. Both the experimental results and FEA studies
show that the diffusion effect is insufficient to explain the observed linear
pressure-dependent behavior of T$_1$.
