An ideal gas is subjected to a thermodynamic process $PV^{2.5} = 0.40$ where $P$ is in $Pa$ and $V$ is in $m^3$.What is the slope of the $P-V$ curve with volume plotted against $x-$ axis at $V=1\, m^3$ ?
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$\mathrm{PV}^{2.5}=0.40$
$\mathrm{P}=0.40 \mathrm{V}^{-2.5}$
$\frac{\mathrm{dP}}{\mathrm{dV}}=0.40\left[-2.5 \mathrm{V}^{-3.5}\right]$
at $\quad V=1$
$\left(\frac{\mathrm{dP}}{\mathrm{dV}}\right)_{\mathrm{V}=1}=-1$
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