A metal jug of negligible thermal capacity contains a mass M of water at a temperature T₁. A dry block of ice (specific latent heat of fusion = Lf) of mass m at 0 °C is dropped into the water (specific heat capacity = c) and begins to melt. At thermal equilibrium, there is no ice in the jug and the temperature of all the water is T₂.
There is no thermal energy transfer between the atmosphere and the water or between the atmosphere and the ice.
Which expression is used to calculate m?
A) Mc(T₁ − T₂) / Lf
B) McT₁ / Lf
C) McT₁ / (Lf + cT₂)
D) Mc(T₁ − T₂) / (Lf + cT₂)
E) Mc(T₁ − T₂) / (Lf + cT₁)
IMAT 2023 · Question 58
Q58 - Changes of state and latent heat
Pinned
The correct answer is D) Mc(T₁ − T₂) / (Lf + cT₂).
No heat is lost, so the heat given out by the warm water equals the heat taken in by the ice.
Water cooling from T₁ to T₂: Mc(T₁ − T₂)
Ice melting at 0 °C: mLf
The melted ice warming from 0 to T₂: mcT₂
So Mc(T₁ − T₂) = m(Lf + cT₂), which gives m = Mc(T₁ − T₂)/(Lf + cT₂).
Option A forgets that the meltwater also has to warm up.
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