Step 1: Determine the total duration and S phase duration.
Given,
\[
\text{Total cell cycle}=24\ \text{hours},
\]
and
\[
\text{S phase}=8\ \text{hours}.
\]
Step 2: Calculate the required fraction.
The fraction of the cell cycle spent in S phase is
\[
\frac{\text{S phase duration}}{\text{Total cell cycle duration}}
=
\frac{8}{24}
=
\frac13.
\]
Hence,
\[
\boxed{\frac13}
\]
is the required fraction.
Therefore,
\[
\boxed{(B)}
\]
is the correct answer.