# physics

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A 55.0 g ice cube, initially at 0°C, is dropped into a Styrofoam cup containing 318 g of water, initially at 18.2°C. What is the final temperature of the water, if no heat is transferred to the Styrofoam or the surroundings?

• physics -

Heat of fusion is the amount of heat energy required to change the state of a substance from solid to liquid.
λ = 335000 J/kg is heat of fusion of water-ice
c = 4185.5 J/(kg•K) is heat capacity of water
Q1 = λ•m1
Q2 =c•m1 •(t-t1) =c•m1•t
Q3 = c•m2 •(t2-t) .
Q1+Q2 = Q3
λ•m1 + c•m1•t = c•m2 •(t2-t),
λ•m1 + c•m1•t = c•m2 •t2 - c•m2 •t,
c•m1•t+ c•m2 •t = c•m2 •t2 - λ•m1

t = (c•m2•t2 - λ•m1)/[c•(m1+m2)] =( 4 180•0.318•18.2 -335000•0.055)/[4180•(0.335•0.055)] = 3.7 oC

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