  It has been conjectured that the internal energy density of the Potts model
on a semi-infinite strip with a width $L$ does not have any finite-size
corrections at the critical point $K=K_c$. By factorizing the transfer matrix
for the kagome lattice with larger widths, we have found that this conjecture
is not correct in that the internal energy density slightly varies with $L$ at
the critical point. From this size dependence of the internal energy density,
we obtain an upper bound as $K_c < 1.0565615$, which is close to a recent
estimate $K_c^{\rm JS} = 1.0565600(7)$ by Jacobsen and Scullard
[arXiv:1204.0622]. We also obtain a lower bound as $K_c > 1.0560$ by
calculating the correlation length along the strips.
