Four 2 cm × 2 cm × 2 cm cubes of ice are removed from a refrigerator and placed in 200 ml of a drink at 10^ ^ ^ C . Determine the amount of ice melted, given that the ice cubes do not melt completely. Assume that the

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Quantrex Academy · Accepted Answer

Correct answer: B. 24.7 g

Since the ice cubes do not melt completely, the final temperature of the mixture is

0^{}^{{}^{\circ}} \text{C}

.

Mass of the drink is given by:

m_d = V_d \times \rho_d = 200 \times 10^{-6} \text{ m}^3 \times 1000 \text{ kg m}^{-3} = 0.2 \text{ kg}

Heat lost by the drink in cooling from

10^{}^{{}^{\circ}} \text{C}

to

0^{}^{{}^{\circ}} \text{C}

is:

Q = m_d c_d \Delta T = 0.2 \times 4200 \times (10 - 0) = 8400 \text{ J}

Let

m

be the mass of the ice melted. Assuming the initial temperature of the ice is

0^{}^{{}^{\circ}} \text{C}

, the heat gained by the ice to melt is:

Q = m L_f = m \times 3.4 \times 10^5 \text{ J}

By the principle of calorimetry, heat lost by the drink equals heat gained by the ice:

m \times 3.4 \times 10^5 = 8400

m = \dfrac{8400}{3.4 \times 10^5} \text{ kg} = \dfrac{84}{3.4} \text{ g} \approx 24.7 \text{ g}

Four 2 cm × 2 cm × 2 cm cubes of ice are removed from a...

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