  We constrain the dark energy equation of state parameter, $w$, using the
power spectrum of the thermal Sunyaev-Zeldovich (tSZ) effect. We improve upon
previous analyses by taking into account the trispectrum in the covariance
matrix and marginalising over the foreground parameters, the correlated noise,
the mass bias $B$ in the Planck universal pressure profile, and all the
relevant cosmological parameters (i.e., not just $\Omega_{\mathrm{m}}$ and
$\sigma_8$). We find that the amplitude of the tSZ power spectrum at
$\ell\lesssim 10^3$ depends primarily on $F\equiv
\sigma_{8}(\Omega_{{\mathrm{m}}}/B)^{0.40}h^{-0.21}$, where $B$ is related to
more commonly used variable $b$ by $B=(1-b)^{-1}$. We measure this parameter
with 2.6\% precision, $F=0.460\pm 0.012$ (68% CL). By fixing the bias to
$B=1.25$ and adding the local determination of the Hubble constant $H_0$ and
the amplitude of the primordial power spectrum constrained by the Planck Cosmic
Microwave Background (CMB) data, we find $w=-1.10\pm0.12$,
$\sigma_{\mathrm{8}}=0.802\pm0.037$, and $\Omega_{{\mathrm{m}}}=0.265\pm0.022$
(68% CL). Our limit on $w$ is consistent with and is as tight as that from the
distance-alone constraint from the CMB and $H_0$. Finally, by combining the tSZ
power spectrum and the CMB data we find, in the $\Lambda$ Cold Dark Matter
(CDM) model, the mass bias of $B=1.71\pm 0.17$, i.e., $1-b=0.58\pm 0.06$ (68%
CL).
