Calculate the work done if 1 mole of certain gas compressed isothermally and reversibly at 300 K from initial pressure $x$ bar to final pressure $2 x$ bar $\left[\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right]$

Calculate the standard enthalpy change of following reaction.

$$ \begin{aligned} & \mathrm{CH}_{4(\mathrm{~s})}+2 \mathrm{O}_{2(\mathrm{~g})} \rightarrow \mathrm{CO}_{2(\mathrm{~g})}+2 \mathrm{H}_2 \mathrm{O}_{(\ell)} \\ & \text { if } \Delta_{\mathrm{f}} \mathrm{H}^{-}\left(\mathrm{CH}_4\right)=-75 \mathrm{~kJ} \mathrm{~mol}^{-1} \end{aligned} $$

$$ \Delta_{\mathrm{f}} \mathrm{H}^*\left(\mathrm{CO}_2\right)=-390 \mathrm{~kJ} \mathrm{~mol}^{-1} $$

$$ \Delta_{\mathrm{r}} \mathrm{H}^{\circ}\left(\mathrm{H}_2 \mathrm{O}\right)=-286 \mathrm{~kJ} \mathrm{~mol}^{-1} $$

Calculate the change in internal energy of the system if work done by the system is 18 joule and absorbs heat 50 joule in a particular reaction.