Calculating Heat Required for Ice Cube Transformation

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Boozehound
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How much heat is required to change a 46.6 g ice cube from ice at -12.5°C to water at 53°C? (if necessary, use cice=2090 J/kg°C and csteam= 2010 J/kg°C)

then i used Q=cmt and Q=mL

Q=(2090)(.0466)(12.5)=1217.425J
Q=(.0466)(33.5E4)=15611J
Q=(2010)(.0466)(53)=4964.298J

then when i add all the numbers up i get 21792.723J total but the answer is wrong. i don't know if I am using the formulas in the wrong order or what. I've done these problems in chemistry but its been a couple years since i took one of those courses. any help is appreciated.
 
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You use C_water, not C_steam for the last calculation (C_water is 4180)