The final temperature of iron and water must be equal to 1000C otherwise no vaporization can take place.
Assuming no heat lost to the environment:
Heat lost by iron = M*C*dT = 50*0.45*(152-100) = 1170 J
Heat gained by water = M*C*dT = 20*4.21*(100-90) = 842 J
At this point, excess heat energy = 1170-842 = 328 J
This much energy is used in vaporizing the water.
Assume that 'x' g of water is vaporized.
Using equation:
m*dHvap = Excess energy
Putting values:
x*(40700/18) = 328
Solving we get:
x = 0.145 g
Hope this helps !
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