A .350 kg of ice is initially at temperature of -12 C. How much heat is required to melt two-third the mass of the ice only?
Q = mcT
here, meting the ice means we need to first bring the temperature from -12 C to 0 C then change the phase to water.
It is very obvious that the whole mass of ice will go to 0 C but only 2/3 of it will melt.
_______________
so,
Q = mcT + mLf
where, Lf is heat of fusion
c is specific heat of ice = 2090 J / Kg C
so,
Q = 0.350 * 2090 * 12 + 0.350 * 3.33e5 * 2/3
Q = 8778 + 77700
Q = 86478 J
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