A metal vessel of negligible heat capacity contains of water at

PHYSICS · Subjective · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

A metal vessel of negligible heat capacity contains 300 g300\,\text{g} of water at 40 ∘C40\,^{\circ}\text{C}. An ice cube of mass 60 g60\,\text{g} at −10 ∘C-10\,^{\circ}\text{C} is dropped into the vessel. Assuming no heat loss to the surroundings, calculate the final equilibrium temperature of the system and state clearly whether any ice remains unmelted. Take: • Specific heat capacity of water =4.2×103 J kg−1 K−1= 4.2\times10^{3}\,\text{J kg}^{-1}\,\text{K}^{-1} • Specific heat capacity of ice =2.1×103 J kg−1 K−1= 2.1\times10^{3}\,\text{J kg}^{-1}\,\text{K}^{-1} • Latent heat of fusion of ice =3.34×105 J kg−1= 3.34\times10^{5}\,\text{J kg}^{-1}.

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