The water is already at its boiling point [tex](T=100^{\circ}C)[/tex], therefore we don't need additional heat to increase its temperature. Instead, we have to give the heat necessary to make it evaporate. The energy needed is equal to
[tex]Q=m L_v[/tex]
where
m is the mass of the water
Lv is the latent heat of evaporation
The latent heat of evaporation of water is [tex]L_v = 2265 J/g[/tex], and the mass of this sample of water is [tex]m=18.0 g[/tex], therefore the heat needed to vaporize the water is
[tex]Q=mL_v = (18.0 g)(2265 J/g)=4.08 \cdot 10^4 J =40.8 kJ[/tex]
