A 124 g ice cube at 0◦C is placed in 777 g of water at 53◦C. What is the final temperature of the mixture? The specific heat of water is 4186 J/kg · ◦C and its latent heat of fusion is 3.33 × 105 J/kg . Answer in units of ◦C.

Let final temp be T.

Heat gained by ice=m(heat of fusion +CdT)

=0.124[3.33*10^{5} +4186*(T-0)]

Heal lost by water=mCdT

=0.777*4186*(53-T)

Heat lost by ice=heat gained by water

0.124[3.33*10^{5} +4186*(T-0)] =0.777*4186*(53-T)

T=34.76 C

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