If $\Delta H$ is the change in enthalpy and $\Delta E$ is the change in internal energy accompanying a gaseous reaction,which of the following is true?

$\Delta_{vap} H^{\ominus}$ for water is $+40.49 \ kJ \ mol^{-1}$ at $1 \ bar$ and $100^{\circ} C$. The change in internal energy for this vaporization under the same conditions is . . . . . . . . . . $kJ \ mol^{-1}$. (Integer answer) (Given $R = 8.3 \ J \ K^{-1} \ mol^{-1}$)

Which one of the following is applicable for an adiabatic expansion of an ideal gas?

The correct relationship is

The $\Delta U^{\theta}$ of combustion of methane is $-X \ kJ \ mol^{-1}.$ The value of $\Delta H^{\theta}$ is

Express the change in internal energy of a system when
$(i)$ No heat is absorbed by the system from the surroundings,but work $(w)$ is done on the system. What type of wall does the system have?
$(ii)$ No work is done on the system,but $q$ amount of heat is taken out from the system and given to the surroundings. What type of wall does the system have?
$(iii)$ $w$ amount of work is done by the system and $q$ amount of heat is supplied to the system. What type of system would it be?