Question

Fifty grams of ice at 0◦ c is placed in a thermos bottle containing one hundred grams of water at 6◦
c. how many grams of ice will melt? the heat of fusion of water is 333 kj/kg and the speci fic heat is 4190 j/kg · k

Answer 1

7.55g (3s.f.)

All the water will cool down to 0°C, which requires 0.419*6 = 2.514kJ of heat to be removed. This requires 2.514/0.333 = 7.55g of ice to melt.

Answer 2

The amount of water that will melt at the given quantity of heat is 75.5 g.

The given parameters;

• mass of the ice = 50 g
• temperature of the ice = 0 ⁰C
• mass of water, = 100 g
• temperature of water, = 6 ⁰C

The heat required to melt the given water is calculated as follows;

$Q = 4190 \ \frac{J}{kg \ K} \times (6-0)\\\\Q = 25140 \ J/kg$

The amount of water that will melt at the given quantity of heat is calculated as follows;

$n(333,000) = Q\\\\n = \frac{25140}{333,000} \\\\n = 0.0755 \ kg\\\\n = 75.5 \ g$

Thus, the amount of water that will melt at the given quantity of heat is 75.5 g.

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