Answer :

The 100 grams of ice at 0 °C is placed in 500 grams of water at 50 °C.  the final temperature is 29 °C .

The specific heat equation is given as :

q = mc ΔT

specific heat of water , c = 4.18 J/g °C

q = n ΔHfusion

heat of fusion of water = 6.01 kJ /mol

moles of water in 100 g of water = 100 / 18 = 5.55 mol

heat needed from solid 0 °C to liquid 0 °C .

q1 = 5.55 × 6.01 = 33.36 kJ

therefore, q1 + q2 = - q3

33.36 + mc ΔT = - mc ΔT

33.36 + 100 × 4.18 (T - 0) = - 500 × 4.18 (T - 25)

33.36 + 418 T = - 2090  ( T - 25 )

33.36 + 418 T = -2090 T + 52250

2508 T = 52216.6

T = 29 °C

Thus,  The 100 grams of ice at 0 °C is placed in 500 grams of water at 50 °C.  the final temperature is 29 °C

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