An ideal gas undergoes a process maintaining relation between pressure $(P)$ and $\operatorname{volume}(V)$ as $P=P_{\mathrm{o}}\left(1+\left(\frac{V_{\mathrm{o}}}{V}\right)^2\right)^{-1}$, where $P_{\mathrm{o}}$ and $V_{\mathrm{o}}$ are constants. If two samples $A$ and $B$ (two moles each) with initial volumes $V_{\mathrm{o}}$ and $3 V_{\mathrm{o}}$ respectively undergo above mentioned process and attain same pressure, then the difference at the temperatures of these samples, $T_B-T_A$ is $\_\_\_\_$ .
( $R=$ gas constant)
- A
$\frac{9 P_{\mathrm{o}} V_{\mathrm{o}}}{8 R}$
- B
$\frac{11 P_{\mathrm{o}} V_{\mathrm{o}}}{10 R}$
- C
$$ \frac{7 P_{\mathrm{o}} V_{\mathrm{o}}}{6 R} $$
- D
$$ \frac{13 P_{\mathrm{o}} V_{\mathrm{o}}}{11 R} $$
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