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Energy used = 10125 J
mass of water vaporized = 4.5g
since all energy are used in only vaporizing and not in increasing temperature, all energy are stored in steam as latent heat of steam.

latent heat = 10125 J/ 4.5g = 2250 J/g OR 2250 kJ/kg
Heat: mL (mass*specific latent heat)
So, 10125=4.5*L
-> L= 10125/4.5
=> L= 2250J/Kg K