$(1)$
\[
\begin{align}
p=\frac{1}{v}
=\frac{p}{RT}
&=\frac{0.1013\times10^6}{287\times288.15}\\
&=1.2249\, \rm{kg/m}^3\\
\end{align}\]
\[\begin{align}
m=pv
&=1.2249\times6.0\\
&=7.3495\,\rm{kg}\\
\end{align}\]
\[
G=\frac{m}{60\,\rm{s}}=0.1225\,\rm{kg/s}
\]
$(2)$
\[
-\dot{L}=G\Delta h\]
\[
\begin{align}
\Delta h=-\frac{\dot{L}}{G}
&=-\frac{7\times10^3}{0.12249}\\
&=-57.147\times10^3\\
&=-57.1\,\rm{kJ/kg}
\end{align}\]
