In a heat insulated vessel there is tap water of 1 5 ∘ C . We place in it n ice cubes of − 1 5 ∘ C taken out of the deep-freezer. S i ce = 2 S w a t er . Each ice cube has same mass as mass of w

Question

In a heat insulated vessel there is tap water of 1 5 ∘ C . We place in it n ice cubes of − 1 5 ∘ C taken out of the deep-freezer. S i ce ​ = 2 S w a t er ​ ​ . Each ice cube has same mass as mass of water in vessel.

TestHub · Accepted Answer

Let water mass be m and its specific heat S.
$Q_{w} = 15 m S$
$Q_{i} = 15 nm S /2$
For one cube, warming ice needs half the heat released by water; surplus heat melts some ice.
$n = 1 : Q_{i} = Q_{w} /2$
For two cubes, the heat quantities match. Both reach freezing temperature without phase change.
$n = 2 : Q_{i} = Q_{w}$
$m S Δ T = 2 m (S /2) Δ T^{'}$
$Δ T^{'} = Δ T$
Thus A and D are correct.

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