_{+}={}_{2}{F_{1}}\left( {\left[ {-\frac{1}{2},\,\frac{{-n}}{{2(n-1)}}}%
\right] ,\,\left[ {\frac{{n-2}}{{2(n-1)}}}\right] ,\,1-}\Gamma
_{+}^{2}\right) ,$$

Here, we are in a position to check the first law of thermodynamics for various horizon topology. At first we obtain the finite mass $M$ as a function of the entropy and electric charge as the extensive quantities. Straightforward calculations show that $$M\left( S,Q\right) =\frac{(n-1){{r_{+}^{n}}}}{{48\pi \alpha }}\left[ \left(
1+\frac{k\alpha }{r_{+}^{2}}\right) ^{3}-1\right] -\frac{{\Lambda {r_{+}^{n}}%
}}{8\pi {n}}-\Theta ,  \label{Smark1}$$where$$\Theta =\left\{
\begin{array}{cc}
\frac{{{\beta ^{2}r_{+}^{n}}}}{16\pi {n}}+\frac{{\beta q}}{8\pi }\left. {%
\int }\left( {{\sqrt{Lw}-{\frac{{1}}{\sqrt{Lw}}}}}\right) {dr}\right\vert
_{r_{+}}, & \text{ENED} \\
-\frac{{{\beta ^{2}r_{+}^{n}}}}{2\pi {n}}+\frac{{\beta }^{2}}{2\pi }\left.
\int {\,{r^{n-1}}}\left[ \Gamma -{\ln \left( \frac{\Gamma {+1}}{2}\right) }%
\right] {dr}\right\vert _{r_{+}}, & \text{LNED}%
\end{array}%
\right. .$$

Now, we use the first law to define temperature and electric potential as the intensive parameters conjugate to the entropy and electric charge $$\begin{aligned}
&&T=\left( \frac{\partial M}{\partial S}\right) _{Q}=\frac{\left( \frac{%
\partial M}{\partial r_{+}}\right) _{Q}}{\left( \frac{\partial S}{\partial
r_{+}}\right) _{Q}},  \label{Tk} \\
&&\Phi =\left( \frac{\partial M}{\partial Q}\right) _{S}=\frac{\left( \frac{%
\partial M}{\partial q}\right) _{r_{+}}}{\left( \frac{\partial Q}{\partial q}%
\right) _{r_{+}}}.  \label{Phik}\end{aligned}$$

Numerical analysis shows that Eqs. (\[Tk\]) and (\[Phik\]) are equal to Eqs. (\[T2\]) and (\[Pot\]), respectively, and therefore we deduce that these quantities satisfy the first law of thermodynamics $$dM=TdS+\Phi dQ.  \label{FirstLaw}$$

$%
\begin{array}{cc}
\epsfxsize=8cm \epsffile{Cvsralpha01.eps} & \epsfxsize=8cm %
\epsffile{Hvsralpha01.eps}%
