Question

Water at 100°C is poured in a bucket containing 4 kg of crushed ice at 0°C, such that all the ice melts and the final temperature recorded is 0°C. Calculate the amount of hot water added to the ice.

[Take the specific heat capacity of water = 4200 Jkg⁻¹K⁻¹ and sp. latent heat of ice = 336000 Jkg⁻¹].

Answer 1

Let the mass of hot water = x kg

Heat given out by hot water = mcθ_f

\[=x \times 4200 \frac{\mathrm{~J}}{\mathrm{~kg} \mathrm{~K}} \times 100 \mathrm{~K}\]

Heat absorbed by ice to form water at 0°C = mL

= 4 kg × 336000 Jkg⁻¹

By the principle of calorimetry,

Heat given out by hot water = Heat absorbed by ice

\[\Rightarrow x \times 4200 \frac{\mathrm{~J}}{\mathrm{~kg} \mathrm{~K}} \times 100 \mathrm{~K} =4 \mathrm{~kg} \times 336000 \mathrm{Jkg}^{-1}\]

\[x =\frac{4 \times 336000}{4200 \times 100} \mathrm{~kg}\]

∴ x = 3.2 kg