Change in internal energy for the heating and vaporisation of water What is the value of change in internal energy at $\pu{1atm}$ in the process $$\ce{H2O(l,$323\ \mathrm K$)-&gt;H2O(g,$423\ \mathrm K$)}$$
  given $C_{\mathrm m,V}(\ce{H2O,l})=\pu{75.0 J K^{-1} mol^{-1}}$ and $C_{\mathrm m,p}(\ce{H2O,g})=\pu{33.314 J K^{-1} mol^{-1}}$
  
  a. $\pu{42.91 kJ/mol}$
  b. $\pu{43086 kJ/mol}$
  c. $\pu{42.6 kJ/mol}$
  d. $\pu{49.6 kJ/mol}$


I tried to use the First Law here. For chemical reaction I found $\Delta n_\mathrm g$ to be $1$ and the heat of the reaction $\Delta H$ is given as $\pu{40.7 kJ mol-1}$. However, I am not able to use the specific heat data given in the question. What am I doing wrong here?

I am getting stuck in phase change reactions, particularly in using $C_p$ and $C_V$ here. I know the First Law will work, but how do we use $C_p$ and $C_V$ in such reactions?
The easiest way to do this problem is to first determine the  change in enthalpy for this constant pressure process.  Do you think you can do that?  Then determine the change in PV between the initial and final states.